Ben Lund, Thresholds for incidence properties in finite vector spaces
Ben Lund, Thresholds for incidence properties in finite vector spaces
Suppose that
Suppose that
In 1982 Galvin, Rival, and Sands proved that in
In 1975, Szemerédi proved that for every real number
The first-order model checking problem for finite graphs asks, given a graph G and a first-order sentence
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
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 …