Immersions in highly edge connected graphs
Combinatorics
2014-01-14 v3
Abstract
We consider the problem of how much edge connectivity is necessary to force a graph G to contain a fixed graph H as an immersion. We show that if the maximum degree in H is D, then all the examples of D-edge connected graphs which do not contain H as a weak immersion must have a tree-like decomposition called a tree-cut decomposition of bounded width. If we consider strong immersions, then it is easy to see that there are arbitrarily highly edge connected graphs which do not contain a fixed clique K_t as a strong immersion. We give a structure theorem which roughly characterizes those highly edge connected graphs which do not contain K_t as a strong immersion.
Keywords
Cite
@article{arxiv.1305.1331,
title = {Immersions in highly edge connected graphs},
author = {Daniel Marx and Paul Wollan},
journal= {arXiv preprint arXiv:1305.1331},
year = {2014}
}