An Improved Planar Graph Product Structure Theorem

Author:

Ueckerdt Torsten,Wood David,Yi Wendy

Abstract

Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth at most 8" by "simple treewidth at most 6".

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Product Structure Extension of the Alon–Seymour–Thomas Theorem;SIAM Journal on Discrete Mathematics;2024-07-09

2. Bounded-Degree Planar Graphs Do Not Have Bounded-Degree Product Structure;The Electronic Journal of Combinatorics;2024-06-14

3. Shallow Minors, Graph Products, and Beyond-Planar Graphs;SIAM Journal on Discrete Mathematics;2024-03-13

4. Product Structure of Graph Classes with Bounded Treewidth;MATRIX Book Series;2024

5. Product structure of graph classes with bounded treewidth;Combinatorics, Probability and Computing;2023-12-07

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