Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656806 | Journal of Combinatorial Theory, Series B | 2015 | 20 Pages |
Abstract
We present an easy structure theorem for graphs which do not admit an immersion of the complete graph KtKt. 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
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Paul Wollan,