Tight upper bound on the number of edges in a bipartite K3,3-free or K5-free graph with an application

Authors:
Zhi-Zhong Chen;Shiqing Zhang
Affiliations:
Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan;Department of Computers, Dandong Institute of Technical Skills, Dandong City, People's Republic of China
Venue:
Information Processing Letters
Year:
2002

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Abstract

We show that an n-vertex bipartite K3,3-free graph with n ≥ 3 has at most 2n - 4 edges and that an n-vertex bipartite K5-free graph with n ≥ 5 has at most 3n - 9 edges. These bounds are also tight. We then use the bound on the number of edges in a K3,3-free graph to extend two known NC algorithms for planar graphs to K3,3-free graphs.