Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs
Combinatorics
2019-03-26 v1
Abstract
For a bipartite graph G, let h(G) be the largest t such that either G or the bipartite complement of G contain K_{t,t}. For a class F of graphs, let h(F)= min {h(G): G\in F}. We say that a bipartite graph H is strongly acyclic if neither H nor its bipartite complement contain a cycle. By Forb(n, H) we denote a set of bipartite graphs with parts of sizes n each, that do not contain H as an induced bipartite subgraph respecting the sides. One can easily show that h(Forb(n,H))= O(n^{1-s}) for a positive s if H is not strongly acyclic. Here, we prove that h(Forb(n, H)) is linear in n for all strongly acyclic graphs except for four graphs.
Keywords
Cite
@article{arxiv.1903.09725,
title = {Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs},
author = {Maria Axenovich and Casey Tompkins and Lea Weber},
journal= {arXiv preprint arXiv:1903.09725},
year = {2019}
}