English

Rooted grid minors

Combinatorics 2013-08-01 v1

Abstract

Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is a set of vertices of cardinality k that cannot be separated from the tangle by any separation of order less than k, then G has a large grid minor containing Z, in which the members of Z all belong to the outside of the grid. This is a lemma for use in a later paper.

Keywords

Cite

@article{arxiv.1307.8138,
  title  = {Rooted grid minors},
  author = {Dániel Marx and Paul Seymour and Paul Wollan},
  journal= {arXiv preprint arXiv:1307.8138},
  year   = {2013}
}
R2 v1 2026-06-22T01:00:53.568Z