An improved planar graph product structure theorem

TL;DR

This paper improves a structural theorem for planar graphs by reducing the bound on simple treewidth from 8 to 6, enhancing our understanding of their product structure.

Contribution

The authors strengthen the existing product structure theorem for planar graphs by lowering the simple treewidth bound from 8 to 6.

Findings

Reduced the simple treewidth bound from 8 to 6 for planar graph product structures.

Maintained the existence of a graph H with bounded simple treewidth and a path P such that G is a subgraph of H ⊠ P.

Enhanced the theoretical understanding of planar graph decompositions.

Abstract

Dujmovi\'c, 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".