Prosenjit Bose ; Vida Dujmović ; Mehrnoosh Javarsineh ; Pat Morin ; David R. Wood - Separating layered treewidth and row treewidth

dmtcs:7458 - Discrete Mathematics & Theoretical Computer Science, May 13, 2022, vol. 24, no. 1 - https://doi.org/10.46298/dmtcs.7458
Separating layered treewidth and row treewidth

Authors: Prosenjit Bose ; Vida Dujmović ; Mehrnoosh Javarsineh ; Pat Morin ; David R. Wood

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.


Volume: vol. 24, no. 1
Section: Graph Theory
Published on: May 13, 2022
Accepted on: April 12, 2022
Submitted on: May 5, 2021
Keywords: Mathematics - Combinatorics,Computer Science - Discrete Mathematics


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