The Erd\H{o}s-Hajnal Conjecture for Long Holes and Anti-holes
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چکیده
Erdős and Hajnal conjectured that, for every graph H , there exists a constant cH such that every graph G on n vertices which does not contain any induced copy of H has a clique or a stable set of size nH . We prove that for every k, there exists ck > 0 such that every graph G on n vertices not inducing a cycle of length at least k nor its complement contains a clique or a stable set of size nk .
منابع مشابه
The Erdős-Hajnal Conjecture for Long Holes and Anti-holes
Erdős and Hajnal conjectured that, for every graph H , there exists a constant cH such that every graph G on n vertices which does not contain any induced copy of H has a clique or a stable set of size nH . We prove that for every k, there exists ck > 0 such that every graph G on n vertices not inducing a cycle of length at least k nor its complement contains a clique or a stable set of size nk .
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