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arXiv · 1512.06441

Treewidth of grid subsets

Eli Berger·Zdenek Dvorak·Sergey Norin
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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.

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Eli Berger, Zdenek Dvorak, Sergey Norin. 2015-12-20. Treewidth of grid subsets. https://arxiv.org/abs/1512.06441

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