Bipartite subgraphs

Abstract

It is shown that there exists a positivec so that for any large integerm, any graph with 2m 2edges contains a bipartite subgraph with at least\(m^2 + m/2 + c\sqrt m\) edges. This is tight up to the constantc and settles a problem of Erdös. It is also proved that any triangle-free graph withe>1 edges contains a bipartite subgraph with at least e/2+c′ e 4/5 edges for some absolute positive constantc′. This is tight up to the constantc′.

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Research supported in part by a USA Israeli BSF grant and by the Fund for Basic Research administered by the Israel Academy of Sciences.

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Alon, N. Bipartite subgraphs. Combinatorica 16, 301–311 (1996). https://doi.org/10.1007/BF01261315

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Mathematics Subject Classification (1991)

  • 05C35