The structure of graphs not admitting a fixed immersion
Combinatorics
2014-07-02 v3
Abstract
We present an easy structure theorem for graphs which do not admit an immersion of the complete graph. The theorem motivates the definition of a variation of tree decompositions based on edge cuts instead of vertex cuts which we call tree-cut decompositions. We give a definition for the width of tree-cut decompositions, and using this definition along with the structure theorem for excluded clique immersions, we prove that every graph either has bounded tree-cut width or admits an immersion of a large wall.
Keywords
Cite
@article{arxiv.1302.3867,
title = {The structure of graphs not admitting a fixed immersion},
author = {Paul Wollan},
journal= {arXiv preprint arXiv:1302.3867},
year = {2014}
}