This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Blažek and M. Koman, A minimal problem concerning complete plane graphs, (M. Fiedler, editor), Theory of Graphs and its Applications, Proc. Symp. Smolenice, 1963, Prague 1964, 113–117; MR 30 #4249.
__________, On an extremal problem concerning graphs, Comm. Math. Univ. Carolinae 8 (1967), 49–52; MR 35 #1506.
R. B. Eggleton, Ph.D. thesis, Univ. of Calgary, 1973.
R. B. Eggleton and R. K. Guy, The crossing number of the n-cube, Amer. Math. Soc. Notices 17 (1970), 757.
P. Erdős and R. K. Guy, Crossing number problems Amer. Math. Monthly, to appear in 1972.
P. Erdős and G. Szerkeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463–470.
I. Fáry, On straight line representation of planar graphs, Acta Sci. Math. (Szeqed) 11 (1948), 229–233; MR 10 #136.
R. K. Guy, A combinatorial problem, Nabla (Bull. Malayan Math. Soc.) 7 (1960), 68–72.
_____, The decline and fall of Zarankiewicz's theorem (F. Harary, editor), Proof Techniques in Graph Theory, Academic Press, N.Y., 1969, 63–69.
_____, Sequences associated with a problem of Turán and other problems, Proc. Balatonfüred Combinatorics Conference, 1969, Bolyai János Matematikai Tarsultat, Budapest, 1970, 553–569.
_____, Latest results on crossing numbers, Recent Trends in Graph Theory, Springer, N.Y., 1971, 143–156.
R. K. Guy, and A. Hill, The crossing number of the complement of a circuit, (submitted to) Discrete Math.
R. K. Guy and T. A. Jenkyns, The toroidal crossing number of Km,n, J. Combinatorial Theory 6 (1969), 235–250; MR 38 #5660.
R. K. Guy, T. A. Jenkyns, and J. Schaer, The toroidal crossing number of the complete graph, J. Combinatorial Theory 4 (1968), 376–390; MR 36 #3682.
F. Harary and A. Hill, On the number of crossings in a complete graph, Proc. Edinburgh Math. Soc. (2) 13 (1962–63), 333–338; MR 29 #602.
H. F. Jensen, An upper bound for the rectilinear crossing number of the complete graph, J. Combinatorial Theory, Ser. B, 10 (1971), 212–216.
P. C. Kainen, On a problem of Erdős, J. Combinatorial Theory 5 (1968), 374–377; MR 38 #72.
P. C. Kainen, A lower bound for crossing numbers of graphs with applications to Kn, Kp,q and Q(d), J. Combinatorial Theory, to appear.
_____, On the stable crossing number of cubes, Proc. Amer. Math. Soc., to appear
D. J. Kleitman, The crossing number of K5,n, J. Combinatorial Theory 9 (1970), 315–323.
M. Koman, On the crossing numbers of graphs, Acta Univ. Carolinae, Math. Phys. 10 (1969), 9–46.
K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271–283.
J. W. Moon, On the distribution of crossings in random complete graphs, J. Soc. Indust. App. Math. 13 (1965), 506–510; MR 31 #3357.
T. L. Saaty, The minimum number of intersections in complete graphs, Proc. Nat. Acad. Sci., U.S.A. 52 (1964), 688–690; MR 29 #4045.
_____, Two theorems on the minimum number of intersections for complete graphs, J. Combinatorial Theory 2 (1967), 571–584; MR 35 #2796.
_____, Symmetry and the crossing number for complete graphs, J. Res. Nat. Bureau Standards 73B (1969), 177–186.
W. T. Tutte, How to draw a graph, Proc. London Math. Soc. (3), 13 (1963), 743–767; MR 28 #1610.
_____, Towards a theory of crossing numbers, J. Combinatorial Theory 8 (1970), 45–53.
K. Urbaník, Solution du problème posé par P. Turán, Colloq. Math. 3 (1955), 200–201.
K. Zarankiewicz, On a problem of P. Turán concerning graphs, Fund. Math. 41 (1954), 137–145; Mr 16 #156.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1972 Springer-Verlag
About this paper
Cite this paper
Guy, R.K. (1972). Crossing numbers of graphs. In: Alavi, Y., Lick, D.R., White, A.T. (eds) Graph Theory and Applications. Lecture Notes in Mathematics, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067363
Download citation
DOI: https://doi.org/10.1007/BFb0067363
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06096-3
Online ISBN: 978-3-540-38114-3
eBook Packages: Springer Book Archive