2018/04/03 by Chudnovsky, Maria, Scott, Alex, Seymour, Paul +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.01060
We prove for every graph H there exists a>0 such that, for every graph G with at least two vertices, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least a|G| neighbours, or there are two disjoint sets A,B of at least a|G| vertices such that no edge joins A and B. It follows that for every graph H, there exists c>0 such that for every graph G, if no induced subgraph of G or its complement is a subdivision of H, then G has a clique or stable set of cardinality at least |G|c. This is related to the Erdos-Hajnal conjecture.