Structural properties of bipartite subgraphs

Abstract

This paper establishes sufficient conditions that force a graph to contain a bipartite subgraph with a given structural property. In particular, let $\beta$ be any of the following graph parameters: Hadwiger number, Hajós number, treewidth, pathwidth, and treedepth. In each case, we show that there exists a function $f$ such that every graph $G$ with $\beta (G)\ge f(k)$ contains a bipartite subgraph $\hat{G}\subseteq G$ with $\beta (\hat{G})\ge k$.

After the first release of this paper, we were informed that our main results were already known

References in corpus (1)

• Making a K_4-free graph bipartite