A note on bounds for the cop number using tree decompositions

TL;DR

This paper introduces a new upper bound on the cop number of graphs based on tree decompositions, extending previous bounds that used treewidth, and provides insights into graph pursuit strategies.

Contribution

It presents a novel upper bound on the cop number leveraging tree decompositions, expanding the understanding beyond existing treewidth-based bounds.

Findings

New upper bound on cop number using tree decompositions

Extension of previous bounds based on treewidth

Enhanced understanding of graph pursuit dynamics

Abstract

In this short note, we supply a new upper bound on the cop number in terms of tree decompositions. Our results in some cases extend a previously derived bound on the cop number using treewidth.