Bipartite Subgraphs (final Version; to Appear in Combinatorica)
نویسنده
چکیده
It is shown that there exists a positive c so that for any large integer m, any graph with 2m 2 edges contains a bipartite subgraph with at least m 2 + m=2 + c p m edges. This is tight up to the constant c and settles a problem of Erd} os. It is also proved that any triangle-free graph with e > 1 edges contains a bipartite subgraph with at least e 2 +c 0 e 4=5 edges for some absolute positive constant c 0. This is tight up to the constant c 0 .
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