Suppose that
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In 1982 Galvin, Rival, and Sands proved that in |
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In 1975, Szemerédi proved that for every real number |
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The first-order model checking problem for finite graphs asks, given a graph G and a first-order sentence |
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We introduce an odd coloring of a graph, which was introduced very recently, motivated by parity type colorings of graphs. A proper vertex coloring of graph |
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We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that every F-free induced subgraph of H has chromatic number at most c=c(F). (Here a graph is F-free if it does not contain an induced copy … |
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