Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656932 | Journal of Combinatorial Theory, Series B | 2013 | 14 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics