Complete Graph Minors and the Graph Minor Structure Theorem
Combinatorics
2015-03-19 v2
Abstract
The graph minor structure theorem by Robertson and Seymour shows that every graph that excludes a fixed minor can be constructed by a combination of four ingredients: graphs embedded in a surface of bounded genus, a bounded number of vortices of bounded width, a bounded number of apex vertices, and the clique-sum operation. This paper studies the converse question: What is the maximum order of a complete graph minor in a graph constructed using these four ingredients? Our main result answers this question up to a constant factor.
Cite
@article{arxiv.1105.3549,
title = {Complete Graph Minors and the Graph Minor Structure Theorem},
author = {Gwenaël Joret and David R. Wood},
journal= {arXiv preprint arXiv:1105.3549},
year = {2015}
}