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- W3124101447 abstract "The Ramsey number RX(p,q) for a class of graphs X is the minimum n such that every graph in X with at least n vertices has either a clique of size p or an independent set of size q. We say that Ramsey numbers are linear in X if there is a constant k such that RX(p,q)≤k(p+q) for all p,q. In the present paper we conjecture that if X is a hereditary class defined by finitely many forbidden induced subgraphs, then Ramsey numbers are linear in X if and only if X excludes a forest, a disjoint union of cliques and their complements. We prove the “only if” part of this conjecture and verify the “if” part for a variety of classes. We also apply the notion of linearity to bipartite Ramsey numbers and reveal a number of similarities and differences between the bipartite and non-bipartite case." @default.
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- W3124101447 date "2021-04-01" @default.
- W3124101447 modified "2023-10-14" @default.
- W3124101447 title "Graph classes with linear Ramsey numbers" @default.
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- W3124101447 doi "https://doi.org/10.1016/j.disc.2021.112307" @default.
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