On dense bipartite graphs of girth eight and upper bounds for certain configurations in planar point-line systems

Journal of Combinatorial Theory. Series A

Volumn 77, Issue 2, 1997, Pages 268-278

  De Caen, D ^a   Szekely L A ^b  

^a QUEEN S UNIVERSITY   (Canada)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031071303     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1997.2745     Document Type: Article

References (12)

1. [AWM] F. V. Atkinson, G. A. Watterson, and P. A. D. Moran, A matrix inequality, Quart. J. Math. Oxford 2nd Ser. 11 (1960), 137-140.
2. [CS] D. de Caen and L. A. Székely, The maximum size of 4-and 6-cycle free bipartite graphs on m, n vertices, in "Sets, Graphs and Numbers" (G. Halász et al., Eds.), pp. 135-142, Colloquia Math. Soc. János Bolyai, Vol. 60, North-Holland, Amsterdam, 1991.
3. [ESS] P. Erdos, A. Sárkozy, and V. T. Sós, On product representation of powers, I, European J. Combin. 16 (1995), 567-588.
4. [FP] Z. Füredi and J. Pach, Traces of finite sets: Extremal problems and geometric applications, in "Bolyai Society Mathematical Studies" (P. Frankl et al., Eds.), Vol. 3, pp. 251-282, Budapest, Hungary, 1994.
5. 6-free bipartite graphs and product representation of squares, submitted.
6. [LUW] F. Lazebnik, V. A. Ustimenko, and A. J. Woldar, New constructions of bipartite graphs on m, n vertices with many edges, and without small cycles, J. Combin. Theory Ser. B 61 (1994), 111-117.
7. [PA] J. Pach and P. K. Agarwal, "Combinatorial Geometry," Wiley-Interscience, New York, 1995.
8. [RS] I. Z. Ruzsa and E. Szemerédi, Triple systems with no six points carrying three triangles, in "Infinite and Finite Sets" (A. Hajnal et al., Eds.), pp. 939-945, Colloq. Math. Soc. J. Bolyai, Vol. 11, North-Holland, Amsterdam, 1975.
9. [S] G. N. Sárközy, Cycles in bipartite graphs and an application in number theory, J. Graph Theory 19 (1995), 323-331.
10. [S1] L. A. Székely, Inclusion-exclusion formulae without higher terms, Ars Combin. B 23 (1987), 7-20.
11. [S2] L. A. Székely, Crossing numbers and hard Erdos problems in discrete geometry, Combin. Probab. Comput., to appear.
12. [ST] E. Szemerédi and W. T. Trotter, Jr., Extremal problems in discrete geometry, Combinatorica 3 (1983), 381-392.