Abstract
The conferences in the series of the Japan Conference on Discrete and Computational Geometry, Graphs and Games (\(\hbox {JCDCG}^3\)) have been held annually since 1997, except for 2008. Since 1997, almost one thousand research results have been presented in total at the conferences, and 11 post-conference proceedings and 6 special issues of journals have been published. To celebrate the 20th Anniversary of \(\hbox {JCDCG}^3\), a summary of the notable results published in those proceedings are presented in this article. We focus on six areas such as games and puzzles, dissection and reversibility, foldings and unfoldings, point sets, visibility, and geometric and topological graph theory.
This is a preview of subscription content, access via your institution.




Notes
John H. Conway, a mathematician, is also famous as the inventor of “Game of Life”, and his earlier book “On Numbers and Games” [59].
References
Abbott, T., Abel, Z., Charlton, D., Demaine, E.D., Demaine, M.L., Kominers, S.: Hinged dissections exist. Discrete Comput. Geom. 47(1), 150–186 (2012)
Able, Z., Ballinger, B., Demaine, E.D., Demaine, M.L., Erickson, J., Hesterberg, A., Itoh, H., Kostitsyna, I., Lynch, J., Uehara, R.: Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares. Special Issue on “Discrete and Computational Geometry, Graph and Games”. J. Inf. Process. 25, 610–615 (2017)
Ackerman, E.: On the maximum number of edges in topological graphs with no four pairwise crossing edges. Discrete Comput. Geom. 41, 365–375 (2009)
Agarwal, P.K., Aronov, B., Pach, J., Pollack, R., Sharir, M.: Quasi-planargraphs have a linear number of edges. Combinatorica 17, 1–9 (1997)
Aichholzer, O., Hackl, T., Huemer, C., Hurtado, F., Krasser, H., Vogtenhuber, B.: On the number of plane geometric graphs. Graphs Combin. 23(Suppl 1), 67–84 (2007). https://doi.org/10.1007/s00373-007-0704-5
Aichholzer, O., Hackl, T., Valtr, P., Vogtenhuber, B.: A Note on the Number of General 4-holes in (Perturbed) Grids. In: Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science, vol. 9943, pp. 1–12 (2016)
Ajtai, M., Chvátal, V., Newborn, M., Szemerédi, E.: Crossing-free subgraphs. Theory and practice of combinatorics. North-Holland Math. Stud. 60, 9–12 (1982)
Akiyama, J.: Tile-makers and semi-tile-makers. Am. Math. Mon. 114(7), 602–609 (2007)
Akiyama, J., Alon, N.: Disjoint simplices and geometric hypergraphs. Combinatorial Mathematics. In: Proceedings of the Third International Conference. Ann. N.Y. Acad.Sci., vol. 555, pp. 1–3 (1989)
Akiyama, J., Asano, T., Kano, M. (eds.) Special Issue on the Japan Conference on Discrete and Computational Geometry 2000. Comput. Geom. 24 (2003)
Akiyama, J., Baskoro, E.T., Kano, M. (eds.): Combinatorial Geometry and Graph Theory, Indonesia-Japan Joint Conference, IJCCGGT 2003, Bandung, Indonesia, September 13–16, 2003, Revised Selected Papers, volume 3330 of Lecture Notes in Computer Science. Springer (2005)
Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds.) Discrete Geometry, Combinatorics and Graph Theory, 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18–20, 2005, Xi’an, China, November 22–24, 2005, Revised Selected Papers, volume 4381 of Lecture Notes in Computer Science. Springer (2007)
Akiyama, J., Demaine, E.D., Langerman S.: Polyhedral Characterization of Reversible Hinged Dissection, in this volume of Graph and Combinatorics. https://link.springer.com/article/10.1007/s00373-019-02041-2 (2020)
Akiyama, J., Ito, H., Sakai, T. (eds.): Discrete and Computational Geometry and Graphs—16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17–19, 2013, Revised Selected Papers, Lecture Notes in Computer Science, vol. 8845. Springer (2014)
Akiyama, J., Ito, H., Sakai, T. (eds.): Discrete and Computational Geometry and Graphs - 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14–16, 2015, Revised Selected Papers, Lecture Notes in Computer Science, vol. 9943. Springer (2016)
Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds.): Special issue on selected papers from the 20th Japan Conference on Discrete and Computational Geometry, Graphs and Games, JCDCGGG 2017, Tokyo, Japan, this issue of Graphs and Combinatorics. Springer (2020)
Akiyama, J., Jiang, B., Kano, M., Tan, X. (eds.): Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Dalian, China, November 3–6, 2010, Revised Selected Papers, Lecture Notes in Computer Science, vol. 7033. Springer (2011)
Akiyama, J., Kaneko, A., Kano, M., Nakamura, G., Rivera-Campo, E., Tokunaga, S., Urrutia, J.: Radial perfect partitions of convex sets in the plane. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 1–13 (2000)
Akiyama, J., Kano, M. (eds.): Discrete and Computational Geometry, Japanese Conference, JCDCG 2002, Tokyo, Japan, December 6–9, 2002, Revised Papers, Lecture Notes in Computer Science, vol. 2866. Springer (2003)
Akiyama, J., Kano, M., Sakai, T. (eds.): Computational Geometry and Graphs—Thailand-Japan Joint Conference, TJJCCGG 2012, Bangkok, Thailand, December 6–8, 2012, Revised Selected Papers, Lecture Notes in Computer Science, vol. 8296. Springer (2013)
Akiyama, J., Kano, M., Tan, X. (eds.): Special Issue on the Japan Conference on Discrete and Computational Geometry 2004. Comput. Geom., vol. 34 (2006)
Akiyama, J., Kano, M., Tan, X. (eds.): Discrete and Computational Geometry, Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8–11, 2004, Revised Selected Papers, Lecture Notes in Computer Science, vol. 3742. Springer (2005)
Akiyama, J., Kano, M., Urabe, M. (eds.): Discrete and Computational Geometry, Japanese Conference, JCDCG 2000, Tokyo, Japan, November, 22–25, 2000, Revised Papers, Lecture Notes in Computer Science, vol. 2098. Springer (2000)
Akiyama, J., Kano, M., Urabe, M. (eds.): Discrete and Computational Geometry, Japanese Conference, JCDCG’98, Tokyo, Japan, December 9–12, 1998, Revised Papers, Lecture Notes in Computer Science, vol. 1763. Springer (2000)
Akiyama, J., Kuwata, T., Langerman, S., Okawa, K., Sato, I., Shephard, G.C.: Determination of all tessellation polyhedral with regular polygonal faces. Computational geometry, graphs and applications, LNCS 7033, Springer, pp. 1–11 (2011)
Akiyama, J., Langerman, S., Matsunaga, K.: Reversible nets of polyhedral. LNCS 9943, 13–23 (2016)
Akiyama, J., Matsunaga, K.: Treks into Intuitive Geometry. Springer, New York (2015)
Akiyama, J., Mochizuki, R., Mutoh, N., Nakamura, G.: Maximin distance for n points in a unit square or a unit circle. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 9–13 (2003)
Akiyama, J., Nakamura, G.: Dudeney dissections of polygons and polyhedrons—a survey. LNCS 2098, 1–30 (2001)
Akiyama, J., Nakamura, G.: Folding of regular polygons to convex polyhedra I. Equilateral triangles. LNCS 3330, 34–43 (2004)
Akiyama J., Nakamura G., Nozaki A., Ozawa K.: A note on the purely recursive dissection for a sequentially n-divisible square. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 41–52 (2001)
Akiyama, J., Nakamura, G., Nozaki, A., Ozawa, K., Sakai, T.: The optimality of a certain purely recursive dissection for a sequentially n-divisible square. Special issue on the Japan conference on discrete and computational geometry 2000. Comput. Geom. 24, 27–39 (2003)
Akiyama, J., Urrutia, J.: Simple alternating path problem. Discrete Math. 84, 101–103 (1990). https://doi.org/10.1016/0012-365X(90)90276-N
Albert, M.H., Nowakowski, R.J., Wolfe, D.: Lessons in Play: An Introduction to Combinatorial Game Theory. A K Peters, Wellesley (2007)
Alexander, R., Dyson, H., O’Rourke, J.: The foldings of a square to convex polyhedra. LNCS 2866, 38–50 (2003)
Alexandrov, A.D.: Convex Polyhedra. Springer, New York (2005)
Aloupis, G., Bose, P., Collette, S., Demaine, E., Demaine, M., Douïeb, K., Dujmović, V., Iacono, J., Langerman, S., Morin, P.: Common unfoldings of polyominoes and polycubes. LNCS 7033, 44–54 (2011)
Alvarez, V., Nakamoto, A.: Colored quadrangulations with Steiner points. In: Computational Geometry and Graphs. TJJCCGG 2012. Lecture Notes in Computer Science, vol. 8296, pp. 20–29 (2013)
Alvarez, V., Sakai, T., Urrutia, J.: Bichromatic quadrangulations with Steiner points. Graphs Combin. 23(Suppl 1), 85–98 (2007). https://doi.org/10.1007/s00373-007-0715-2
Asano, Y., Demaine, E.D., Demaine, M.L., Hosaka, H., Kawasaki, A., Tachi, T., Takahashi, K.: Folding and punching paper, Special Issue on “Discrete and Computational Geometry, Graph and Games’. J. Inf. Process. 25, 590–600 (2017)
Bárány, I., Károlyi, G.: Problems and results around the Erdős–Szekeres convex polygon theorem. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 91–105 (2001)
Bau, S., Saito, A.: Reduction for 3-connected graph of minimum degree at least four. G&C 23, 135–144 (2007)
Beloch, M.P.: Sulla risoluzione dei problemi di terzo e quarto grado col metodo del ripiegamento della carta. Scritti Matematici Offerti a Luigi Berzolari, Pavia, pp. 93–96 (1936)
Bereg, S., Bose, P., Kirkpatrick, D.: Equitable subdivisions within polygonal regions. Special Issue on the Japan Conference on Discrete and Computational Geometry 2004. Comput. Geom. 34, 20–27 (2006)
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 1-2, 1st edn. Academic Press, London (1982)
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 1–4, 2nd edn. A K Peters, Wellesley (2001)
Bern, M., Hayes, B.: The Complexity of flat origami. In: Proc. 7th ACM-SISM Symp, Discrete Algorithms, ACM/SIAM, New York, pp. 175–183 (1996)
Bespamyatnikh, S.: On partitioning a cake. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 60–71 (2003)
Bespamyatnikh, S., Kirkpatrick, D.: Constrained equitable 3-cuttings. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 72–83 (2003)
Bespamyatnikh, S., Kirkpatrick, D., Snoeyink, J.: Generalizing ham sandwich cuts to equitable subdivisioons. Discrete Comput. Geom. 24, 605–622 (2000)
Bolyai, F.: Tentamen juventutem Maros Vasarhelyini: Typis Collegii Reformatorum per Josephum et Simeonem Kali (in Hungarian) (1832)
Bosboom, J., Demaine, E.D., Hesterberg, A., Lynch, J., Waingarten, Erik.: Mario Kart is hard. In: Akiyama et al. [15], pp. 49–59
Bose, P., Langerman, S.: Weighted ham-sandwich cuts. In: Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol. 3742, pp. 48–53 (2005)
Bremner, D., Hurtado, F., Ramaswami, S., Sacristán, V.: Small strictly convex quadrilateral meshes of point sets. Algorithmica 38, 317–339 (2004). https://doi.org/10.1007/s00453-003-1062-1
Burke, K., Demaine, E.D., Gregg, H., Hearn, R. A., Hesterberg, A., Hoffmann, M., Ito, H., Kostitsyna, I., Leonard, J., Löffler, M., Santiago, A., Schmidt, C., Uehara, R., Uno, Y., Williams, A.: Single-player and two-player buttons and scissors games (extended abstract). In: Akiyama et al. [15], pp. 60–72
Chvátal, V.: A combinatorial theorem in plane geometry. J. Combin. Theory Ser. B 18, 39–41 (1975). https://doi.org/10.1016/0095-8956(75)90061-1
Cohn, M.J.: Economical triangle-square dissection. Geom. Dedicata 3, 447–467 (1975)
Cole, A., Demaine, E.D., Fox-Epstein, E.: On wrapping spheres and cubes with rectangular paper. LNCS 8845, 31–43 (2014)
Conway, J.H.: On Numbers and Games. Academic Press, London (1976)
Demaine, E.: Folding and unfolding linkages. Paper, and polyhedra. LNCS 2098, 113–124 (2001)
Demaine, E.D.: Playing games with algorithms: algorithmic combinatorial game theory. In: MFCS, Lecture Notes in Computer Science, vol. 2136, pp. 18–32. Springer (2001)
Demaine, E.D., Demaine, M.L., Hawksley, A., Ito, H., Loh, P., Manber, S., Stephens, O.: Making polygons by simple folds and one straight cut. In: Proc. CGGA 2010, LNCS 7033, pp. 27–43 (2011)
Demaine, E., Demaine, M., Itoh, J., Nara, C.: Continous flattening of orthogonal polyhedra. LNCS 9943, 85–93 (2016)
Deamine, E., Deamine, M.L., Lubiw, A.: Folding and cutting paper. LNCS 1763, 104–118 (2000)
Demaine, M., Flatland, R., O’Rourke, J.: Epsilon-unfolding orthogonal
Demaine, E. D., Hohenberger, S., Liben-Nowell, D.: Tetris is hard, even to approximate. In: COCOON, Lecture Notes in Computer Science, vol. 2697, pp. 351–363. Springer (2003)
Demaine, E.D., Korman, M., Ku, J.S., Mitchell, J.S.B., Otachi, Y., van Renssen, A., Roeloffzen, M., Uehara, R., Uno, Y.: Symmetric assembly puzzles are hard, beyond a few pieces. In: Akiyama et al. [15], pp. 180–192
Demaine, E.D., Langerman, S.: Bust-a-move/puzzle bobble is NP-complete. In: Akiyama et al. [15], pp. 94–104
Demaine, E.D., O’Rourke, J.: Geometric Folding Algorithms—Linkages, Origami, Polyhedra. Cambridge University Press, Cambridge (2007)
Demaine, E.D., Rudoy, M.: A simple proof that the (n2 − 1)-puzzle is hard. Theor. Comput. Sci. 732, 80–84 (2018)
Demaine, E.D., Rudoy, M.: Tree-residue vertex-breaking: a new tool for proving hardness. In 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018, June 18–20, 2018, Malmö, pp. 32:1–32:14 (2018)
Ding, R., Hosono, K., Urabe, M., Xu, C.: Partitioning a planar point set into empty convex polygons. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 129–134 (2003)
Dudeney, H.E.: Puzzles and prizes, weekly dispatch, April 6–May 4 (1902)
Dudeney, H.E.: The Canterburry Puzzles and Other Curious Problems. W. Heinemann, London (1907)
Dürer, A.: The Painter’s Manual, A Manual of Measurement of Lines, Areas, and Solids by Means of Compass and Ruler Assembled by Albrecht Dürer for the Use of all Lovers of Art with Appropriate Illustrations Arranged to be Printed in the Year MDXXV. Abaris Books, New York, 1997 (1525). English translation by Walter L. Strauss of “Unterweysung der Messung mit dem Zirkel un Richtscheyt in Linien Ebnen uhnd Gantzen Corporen”
Editorial Board of Graphs and Combinatorics (eds.): Special issue on selected papers from the 5th Conference on Graph Theory and Discrete Geometry, GTDG 2001, Manila, Graphs and Combinatorics, vol. 18(4). Springer (2002)
Erdős, P.: On sets of distances of n points. Am. Math. Mon. 53, 248–250 (1946)
Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compos. Math. 2, 463–470 (1935)
Erdős, P., Szekeres, G.: On some extremum problems in elementary geometry. Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 3–4, 53–62 (1961)
Even, S., Tarjan, R.E.: A combinatorial problem which is complete in polynomial space. J. ACM 23(4), 710–719 (1976)
Fisk, S.: A short proof of Chvátal’s watchman theorem. J. Combin. Theory Ser. B 24, 374 (1978). https://doi.org/10.1016/0095-8956(78)90059-X
Frederickson, G.N.: Dissections Plane and Fancy. Cambridge University Press, Cambridge (1997)
Frederickson, G.N.: Hinged Dissections Swinging and Twisting. Cambridge University Press, Cambridge (2002)
Frederickson, G.N.: Geometric dissections that swing and twist. LNCS 2098, 137–148 (2001)
Frederickson, G.N.: Piano-hinged dissections. LNCS 2866, 159–171 (2003)
Frederickson, G.N.: Unexpected twist in geometric dissections. Graph Combin. 23, 245–258 (2007)
Fukui, H., Otachi, Y., Uehara, R., Uno, T., Uno Y.: On complexity of flooding games on graphs with interval representations. In: TJJCCGG, Lecture Notes in Computer Science, vol. 8296, pp. 73–84. Springer (2012)
García-López, J., Nicolás, C.M.: Planar point sets with large minimum convex decompositions. Graphs Combin. 29, 1347–1353 (2013). https://doi.org/10.1007/s00373-012-1181-z
Gardner, M.: Mathematical Games. Scientific American (1957–1981)
Gardner, M.: The 2nd Scientific American Book of Mathematical Puzzles & Diversions. Simon & Schuster, New York (1961)
Gardner, M.: New Mathematical Diversions from Scientific American. Simon & Schuster, New York (1966)
Gardner, M.: The Unexpected Hanging and Other Mathematical Diversions, Chicago University of Chicago Press. Updated with a new afterword and an expanded bibliography 1991 (1969)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Gerwien, P.: Zerachneidung jeder bellebigen Anzahl von gleichen gersdlinigen Flguern in disselben Stucke. J. Reine Angew Math. 10, 228–234 and Taf. III (1833)
Guth, L., Katz, N.H.: On the Erdős distinct distances problem in the plane. Ann. Math. (2) 181, 155–190 (2015). https://doi.org/10.4007/annals.2015.181.1.2
Hearn, R.A., Demaine, E.D.: Games, Puzzles and Computation. A K Peters, Wellesley (2009)
Heredia, V.M., Urrutia, J.: On convex quadrangulations of point sets on the plane. In: Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol. 4381, pp. 38–46 (2007)
Horiyama, T., Itoh, J., Katoh, N., Kobayashi, Y., Nara, C.: Continuous folding of regular dodecahedra. LNCS 9943, 120–131 (2016)
Hosono, K., Rappaport, D., Urabe, M.: On convex decompositions of points. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 149–155 (2001)
Hosono, K., Urabe, M.: A minimal planar point set with specified disjoint empty convex subsets. In: Computational Geometry and Graph Theory. KyotoCGGT 2007. Lecture Notes in Computer Science, vol. 4535, pp. 90–100 (2008)
Huffman, D.A.: Curvature and creases: a primer on paper. IEEE Trans. Comput
Hull, T.: Project Origami, Activities for Exploring Mathematics. A K Peters, Wellesley (2006)
Huzita, H., Scimemi, B.: The algebra of paper folding (origami). In: Huzita, H. (ed.) Proc. 1st Int. Meeting Origami Sci. Tech., pp. 215–222, Ferrara (1989)
Ito, H., (ed.) Special issue on selected papers from the 12th Japan Conference on Computational Geometry and Graphs, JCCGG 2009, Kanazawa, Graphs and Combinatorics, vol. 27(3). Springer (2011)
Ito, H., et al. (eds.) Special issue on selected papers from the 19th Japan Conference on Discrete and Computational Geometry, Graphs and Games, JCDCGGG 2016, Tokyo, Japan. Journal of Information Processing. Information Processing Society of Japan (2017)
Ito, H., Kano, M., Katoh, N., Uno, Y., editors. Computational Geometry and Graph Theory - International Conference, KyotoCGGT 2007, Kyoto, Japan, June 11–15, 2007. Revised Selected Papers, Lecture Notes in Computer Science, vol. 4535. Springer (2008)
Ito, H., Uehara, H., Yokoyama, M.: 2-Dimension ham sandwich theorem for partitioning into three convex pieces. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 129–157 (2000)
Ito, H., Uehara H., Yokoyama M.: NP-completeness of stage illumination problems. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 158–165 (2000)
Itoh, J., Nara, C.: Continuous flattering of platonic polyhedral. LNCS 7033, 108–121 (2011)
Justin, J.: Aspects mathematiques du pliage de papier (Mathematical aspects of paper folding). In: Huzita, H. (ed.) Proc. of 1st Int. Meeting Origami Sci. Tech., pp. 263–277, Ferrara (1989)
Kaneko, A.: On the maximum degree of bipartite embeddings of trees in the plane. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 166–171 (2000)
Kaneko, A., Kano, M.: Balanced partitions of two sets of points in the plane. Comput. Geom. 13, 253–261 (1999)
Kaneko, A., Kano, M.: Generalized balanced partitions of two sets of points in the plane. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 176–186 (2001)
Kaneko, A., Kano, M.: On paths in a complete bipartite geometric graph. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 187–191 (2001)
Kano, M., Merino, C., Urrutia, J.: On plane spanning trees and cycles of multicolored point sets with few intersections. Inf. Process. Lett. 93, 301–306 (2005)
Kano, M., Suzuki, K., Uno, M.: Properly colored geometric matchings and 3-trees without crossings on multicolored points in the plane. In: Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science, vol. 8845, pp. 96–111 (2014)
Kano, M., Uno, M.: General balanced subdivision of two sets of points in the plane. In: Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol. 4381, pp. 79–87 (2007)
Kawasaki, T.: On the relation between mountain-creases and valley-creases of a flat origami, editor, Proc. 1st Int. Meeting Origami Sci. Tech., 229–237, Ferrara, Italy (1989). Unabridged Japanese version in Sasebo College Tech. Rep. (27), pp. 153–157 (1990)
Khramtcova, E., Langerman, S.: Which convex polyhedra can be made by gluing regular hexagons? Graphs Combin., in this volume
Kim, K., Bourne, D., Gupta, S., Krishna, S.S.: Automated process planning for sheet metal bending operations. J. Manuf. Syst 17(5), 338–360 (1998)
Kranakis, E., Krizanc, D., Urrutia, J.: Efficient regular polygon dissections. LNCS 1763, 172–187 (2000)
Lang, R.J.: Origami Design Secrets, Mathematical Methods for an Ancient Art. A K Peters, Wellesley (2003)
Langerman, S., Winslow, A.: A complete classification of tile-makers. In: Abstracts from the 18th Japan Conference on Discrete and Computational Geometry and Graphs. Kyoto (2015)
Larson, L.C.: Problem-solving through problems, pp. 200–201. Springer, New York (1983)
Leaños, J., Merino, C., Salazar, G., Urrutia, J.: Spanning trees of multicoloured point sets with few intersections. In: Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol. 3330, pp. 113–122 (2005)
Leighton, T.: Complexity Issues in VLSI, Foundations of Computing Series. MIT Press, Cambridge (1983)
Lemon, D.: The Illustrated Book of Puzzles. Saxon, London (1890)
Levitin, A., Levitin, M.: Algorithmic Puzzles. Oxford University Press, Oxford (2011)
Lichtenstein, D., Sipser, M.: GO is PSPACE hard. In: FOCS. IEEE Computer Society, pp. 48–54 (1978)
Lindgren, H.: Recreational Problems in Geometric Dissections and How to Solve Them. Dover, New York (1972)
Lowry, M.: Solution to question 269, [proposed] by Mr. W. Wallace. In: Leybourn, T. (ed.) Mathematical Repository, vol. 3, part 1. W. Glendinning, London, pp. 44–46 (1814)
Madachy, J.S.: Geometric Dissections, In Madachy’s Mathematical Recreations, ch. 1, pp. 16–33. Dover, New York (1979)
Nishimura, N.: Introduction to reconfiguration. Algorithms 11(4), 52 (2018)
O’Rourke, J.: Folding and unfolding in computational geometry. LNCS 1763, 258–266 (1998)
O’Rourke, J.: Folding polygons to convex polyhedra, Understanding Geometry for a Changing World, National Council of Teachers of Mathematics, 71th Yearbook. National Council of Teachers of Mathematics, pp. 77–87 (2009)
O’Rourke, J.: How to Fold It, The Mathematics of Linkages, Origami, and Polyhedra. Cambridge University Press, Cambridge (2011)
O’Rourke, J.: On folding a polygon to a polyhedron. arXiv:1007.3181vl [cs.CG]. arXiv:1007.3181
O’Rourke, J.: On the development of the intersection of a plane with a polytope. Special Issue on the Japan Conference on Discrete and Computational Geometry 2000. Comput. Geom. 24, 3–10 (2003)
Pach, J.: Crossing numbers. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 267–273 (2000)
Pach, J., Pinchasi, R.: How many unit equilateral triangles can be generated by n points in convex position? Am. Math. Mon. 110, 400–406 (2003)
Pach, J., Radoičić, R., Tóth, G.:Relaxing planarity for topological graphs. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 221–232 (2003)
Pach, J., Radoičić, R., Vondrák, J.: Nearly equal distances and Szemerédi’s regularity lemma. Special Issue on the Japan Conference on Discrete and Computational Geometry 2004. Comput. Geom. 34, 11–19 (2006)
Pach, J., Rubin, N., Tardos G.: Beyond the Richter–Thomassen conjecture. In: Proc. 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016, Arlington). SIAM, pp. 957–968 (2016)
Pach, J., Tardos, G.: Forbidden patterns and unit distances. In: Proceedings of the 21st Annual Symposium on Computational Geometry, pp. 1–9 (2005)
Pach, J., Tardos, G.: Isosceles triangles determined by a planar point set. Special Issue on Graph Theory and Discrete Geometry, Manila 2001. Graphs Combin. 18, 769–779 (2002). https://doi.org/10.1007/s003730200063
Pach, J., Tóth, G.: Disjoint edges in topological graphs. In: Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol. 3330, pp. 133–140 (2005)
Pach, J., de Zeeuw, F.: Distinct distances on algebraic curves in the plane. In: Proc. 30th Symposium on Computational Geometry, pp. 549–557 (2014)
Panckoucke, A.J.: Les Amusements Mathématiques, Chez André-Joseph Panckoucke, Lille (1749)
Pilz, A.: Planar 3-SAT with a clause/variable cycle. Discrete Math. Theor. Comput. Sci. 21(3) (2019)
Rappaport, D.: Tight bounds for visibility matching of f-equal width objects. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 246–250 (2003)
Ratner, D., Warmuth, M.K.: N × N puzzle and related relocation problem. J. Symb. Comput. 10(2), 111–138 (1990)
Richter, R.B., Thomassen, C.: Intersections of curve systems and the crossing number of C5 × C5. Discrete Comput. Geom. 13, 149–159 (1995). https://doi.org/10.1007/BF02574034
Rivera-Campo, E.: A note on the existence of plane spanning trees of geometric graphs. In: Discrete and Computational Geometry. JCDCG’98. Lecture Notes in Computer Science, vol. 1763, pp. 274–277 (2000)
Rokicki, T., Kociemba, H., Davidson, M., Dethridge, J.: The diameter of the Rubik’s cube group is twenty. SIAM Rev. 56(4), 645–670 (2014)
Sakai, T.: Balanced convex partitions of measures in \(\mathbb{R}^2\). Graphs Combin. 18, 169–192 (2002)
Sakai, T., Urrutia, J.: Covering the convex quadrilaterals of point sets. Graphs Combin. 23(Suppl 1), 343–357 (2007). https://doi.org/10.1007/s00373-007-0717-0
Sakai, T., Urrutia, J.: Convex decompositions of point sets in the plane (2019). arXiv:1909.06105
Schaefer, T.J.: On the complexity of some two-person perfect-information games. J. Comput. Syst. Sci. 16(2), 185–225 (1978)
Shephard, G.C.: Convex polytopes with convex nets. Math. Proc. Camb. Philos. soc. 78, 389–403 (1975)
Spencer, J., Szemerédi, E., Trotter, W.T.: Unit distances in the Euclidean plane. In: Bollobás, B. (ed.) Graph Theory and Combinatorics, pp. 293–303. Academic Press, London (1984)
Sugihara, K.: Computer-aided creation of impossible objects and impossible motions. LNCS 4535, 201–212 (2008)
Suk, A.: On the Erdős–Szekeres convex polygon problem. J. Am. Math. Soc. 30, 1047–1053 (2017). https://doi.org/10.1090/jams/869
Suzuki, K.: On the number of intersections of three monochromatic trees in the plane. In: Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol. 2866, pp. 261–272 (2003)
Szekeres, G., Peters, L.: Computer solution to the 17-point Erdős–Szekeres problem. ANZIAM J. 48, 151–164 (2006). https://doi.org/10.1017/S144618110000300X
Tan, X., Zhang, J., Jiang, B.: A characterization of link-2 LR-visibility polygons with applications. In: Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science, vol. 8845, pp. 161–172 (2014)
Tardos, G., Tóth, G.: Crossing stars in topological graphs. In: Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol. 3742, pp. 184–197 (2005)
Tokuyama, T.: Efficient algorithms for the minimum diameter bridge problem. Special Issue on the Japan Conference on Discrete and Computational Geometry 2000. Comput. Geom. 24, 11–18 (2003)
Tokuyama, T.: Recent progress on combinatorics and algorithms for low discrepancy roundings. G&C 23, 359–378 (2007)
Tóth, C.D.: Illuminating both sides of line segments. In: Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol. 2098, pp. 370–380 (2001)
Uehara, R.: A survey and recent results about common developments of two or more boxes. In \(\text{Origami}^6\): Proceedings of the 6th International Meeting on Origami in Science, Mathematics and Education, vol. 1 (Mathematics). American Mathematical Society, pp. 77–84 (2014)
Urrutia, J.: Art gallery and illumination problems. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry. North Holland (Elsevier Science), pp. 973–1027 (2000)
Urrutia, J.: Open problem session, 10th Canadian Conference on Computational Geometry. McGill University, Montreal (1998)
Wallace, W. (ed.): Elements of Geometry, 8th edn. Bell & Bradfute, Edinburgh (1831)
Winkler, P.: Mathematical Mind-Benders. A K Peters, Wellesley (2007)
Winkler, P.: Mathematical Puzzles: A Connoisseur’s Collection. A K Peters, Wellesley (2004)
Winkler, P.: Puzzled. Communications of the ACM (2008–2014)
Wu, L., Ding, R.: Reconfirmation of two results on disjoint empty convex polygons. In: Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol. 4381, pp. 216–220 (2007)
Acknowledgements
Many thanks go to the following people for hosting \(\hbox {JCDCG}^3\) during these 20 years: Tetsuo Asano, Edy Tri Baskoro, Jiang Bo, William Chen, Wanida Hemakul, Mikio Kano, Naoki Katoh, Xueliang Li, Reginaldo Marcelo, Late Narong Punnim, Mari Jo Ruiz and Xuehou Tan.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Research supported by JST CREST Grant Number JPMJCR1402, Japan, and by JSPS KAKENHI Grant Number 17K00017.
Rights and permissions
About this article
Cite this article
Akiyama, J., Ito, H., Sakai, T. et al. Twenty Years of Progress of \(\hbox {JCDCG}^3\). Graphs and Combinatorics 36, 181–203 (2020). https://doi.org/10.1007/s00373-020-02133-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00373-020-02133-4