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 $\beta(G)\geq f(k)$ contains a bipartite subgraph $\hat{G}\subseteq G$ with $\beta(\hat{G})\geq k$.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.12099
 arXiv:
 arXiv:2106.12099
 Bibcode:
 2021arXiv210612099H
 Keywords:

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