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arXiv · 2105.01230

Separating layered treewidth and row treewidth

Prosenjit Bose·Vida Dujmović·Mehrnoosh Javarsineh·Pat Morin·David R. Wood
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Abstract

Layered treewidth and row treewidth are recently introduced graph parameters that have been key ingredients in the solution of several well-known open problems. It follows from the definitions that the layered treewidth of a graph is at most its row treewidth plus 1. Moreover, a minor-closed class has bounded layered treewidth if and only if it has bounded row treewidth. However, it has been open whether row treewidth is bounded by a function of layered treewidth. This paper answers this question in the negative. In particular, for every integer $k$ we describe a graph with layered treewidth 1 and row treewidth $k$. We also prove an analogous result for layered pathwidth and row pathwidth.

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Prosenjit Bose, Vida Dujmović, Mehrnoosh Javarsineh, Pat Morin, David R. Wood. 2021-05-04. Separating layered treewidth and row treewidth. https://doi.org/10.46298/dmtcs.7458

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