Treewidth of grid subsets
Combinatorics
2015-12-22 v1
Abstract
Let Q_n be the graph of n times n times n cube with all non-decreasing diagonals (including the facial ones) in its constituent unit cubes. Suppose that a subset S of V(Q_n) separates the left side of the cube from the right side. We show that S induces a subgraph of tree-width at least n/sqrt{18}-1. We use a generalization of this claim to prove that the vertex set of Q_n cannot be partitioned to two parts, each of them inducing a subgraph of bounded tree-width.
Keywords
Cite
@article{arxiv.1512.06441,
title = {Treewidth of grid subsets},
author = {Eli Berger and Zdenek Dvorak and Sergey Norin},
journal= {arXiv preprint arXiv:1512.06441},
year = {2015}
}
Comments
15 pages, no figures