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Bar 1-Visibility Drawings of 1-Planar Graphs

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Applied Algorithms (ICAA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8321))

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Abstract

A bar 1-visibility drawing of a graph G is a drawing of G where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment between its incident vertices such that each edge crosses at most one bar. A graph G is bar 1-visible if G has a bar 1-visibility drawing. A graph G is 1-planar if G can be drawn in the plane such that each edge has at most one crossing. In this paper we give O(n) time algorithms to find bar 1-visibility drawings of diagonal grid graphs, maximal outer 1-planar graphs, recursive quadrangle 1-planar graphs and pseudo double wheel 1-planar graphs, where n is the number of vertices in the input graph.

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References

  1. Argyriou, E.N., Bekos, M.A., Symvonis, A.: The straight-line RAC drawing problem is NP-hard. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 74–85. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  2. Arikushi, K., Fulek, R., Keszegh, B., Morić, F., Tóth, C.D.: Graphs that admits right angle crossing drawing. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 135–146. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Dean, A.M., Evans, W., Gethner, E., Laison, J.D., Safari, M.: Bar k-visibility graphs. Journal of Graph Algorithms and Applications 11(1), 45–59 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dehkordi, H., Eades, P.: On algorithmic right angle crossing graph drawing. Int. J. Comput. Geometry 22(6), 543–557 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall Inc. (1999)

    Google Scholar 

  6. Di Battista, G., Tamassia, R., Tollis, I.G.: Constrained visibility representation of graphs. Inform. Process. Letters 41, 1–7 (1992)

    Article  MATH  Google Scholar 

  7. Didimo, W., Eades, P., Liotta, G.: Drawing graphs with right angle crossings. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 206–217. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Didimo, W., Eades, P., Liotta, G.: A characterization of complete bipartite RAC graphs. Information Processing Letters 110(16), 687–691 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Eades, P., Liotta, G.: Right angle crossing graphs and 1-planarity. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 148–153. Springer, Heidelberg (2011)

    Google Scholar 

  10. Fabrici, I., Madaras, T.: The structure of 1-planar graphs. Discrete Mathematics 307(7-8), 854–865 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Korzhik, V.P., Mohar, B.: Minimal obstructions for 1-immersions and hardness of 1-planarity testing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 302–312. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Nishizeki, T., Rahman, M.S.: Planar Graph Drawing. Lecture notes series on computing. World Scientific (2004)

    Google Scholar 

  13. Otten, J., Van Wijk, J.G.: Graph representation in interactive layout design. In: The Proceedings of IEEE International Symposium on Circuits and Systems, pp. 914–918 (1978)

    Google Scholar 

  14. Pach, J., Tóth, G.: Graphs drawn with few crossings per edge. Combinatorica 17(3), 427–439 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Selvaraju, P., Pricilla, B.: On cordial labeling: The grid, diagonal grid, structured web graphs. International Journal of Algorithms, Computing and Mathematics 2(1), 5–14 (2009)

    Google Scholar 

  16. Suzuki, Y.: Optimal 1-planar graphs which triangulate other surfaces. Discrete Mathematics 310(1), 6–11 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  17. Tamassia, R., Tollis, I.G.: A unified approach to visibility representations of planar graphs. Discrete and Computational Geometry 1, 321–341 (1986)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, 1000, Bangladesh

    Shaheena Sultana, Md. Saidur Rahman, Arpita Roy & Suraiya Tairin

Authors
  1. Shaheena Sultana
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  2. Md. Saidur Rahman
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  3. Arpita Roy
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  4. Suraiya Tairin
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Editor information

Editors and Affiliations

  1. Computer Science and Engineering, Heritage Institute of Technology, Chowbaga Road, Anandapur, 700107, Kolkata, India

    Prosenjit Gupta

  2. Department of Computer Engineering and Informatics, University of Patras, 26500, Patras, Greece

    Christos Zaroliagis

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© 2014 Springer International Publishing Switzerland

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Sultana, S., Rahman, M.S., Roy, A., Tairin, S. (2014). Bar 1-Visibility Drawings of 1-Planar Graphs. In: Gupta, P., Zaroliagis, C. (eds) Applied Algorithms. ICAA 2014. Lecture Notes in Computer Science, vol 8321. Springer, Cham. https://doi.org/10.1007/978-3-319-04126-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-04126-1_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04125-4

  • Online ISBN: 978-3-319-04126-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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