Clique covering the edges of a locally cobipartite graph

doi:10.1016/S0012-365X(99)00333-7

Discrete Mathematics

Volume 219, Issues 1–3, 28 May 2000, Pages 17-26

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Abstract

We prove that a locally cobipartite graph on n vertices contains a family of at most n cliques that cover its edges. This is related to Opsut's conjecture that states the competition number of a locally cobipartite graph is at most two.

Keywords

Claw free

Cobipartite graph

Competition graph

Edge clique cover

Opsut's conjecture

Cited by (0)

¹: Research partially supported under N.S.A. grant MDA 904-97-1-0101.

²: Research partially supported under an exchange program of the Vice President of Georgia State University.

³: On leave from the Automation and Computing Research Institute of the Hungarian Academy of Sciences.