Capture times in the Bridge-burning Cops and Robbers game

TL;DR

This paper investigates the bridge-burning cops and robbers game, focusing on the maximum capture time when edges are removed after robber traversal, providing insights into the dynamics of this variant.

Contribution

It introduces an analysis of capture times in the bridge-burning cops and robbers game, a novel variant where edges are destroyed after use by the robber.

Findings

Characterization of maximum capture times

Bounds on capture time in various graph classes

Insights into strategic edge removal effects

Abstract

In this paper, we consider a variant of the cops and robbers game on a graph, introduced by Kinnersley and Peterson, in which every time the robber uses an edge, it is removed from the graph, known as bridge-burning cops and robbers. In particular, we study the maximum time it takes the cops to capture the robber.