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- W3082032630 abstract "The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c>0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this paper, we prove a conjecture of Liebenau and Pilipczuk [10], that for every forest H there exists c>0, such that every graph G with |G|>1 contains either an induced copy of H, or a vertex of degree at least c|G|, or two disjoint sets of at least c|G| vertices with no edges between them. It follows that for every forest H there exists c>0 such that, if G contains neither H nor its complement as an induced subgraph, then there is a clique or stable set of cardinality at least |G|c." @default.
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- W3082032630 date "2020-12-01" @default.
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- W3082032630 title "Pure pairs. I. Trees and linear anticomplete pairs" @default.
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- W3082032630 doi "https://doi.org/10.1016/j.aim.2020.107396" @default.
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