The Cat and the Noisy Mouse

TL;DR

This paper studies a pursuit-evasion game on graphs where a cat with partial distance info can catch an invisible mouse, proving the cat wins iff the graph is a forest, extending prior work with new insights.

Contribution

It introduces a variant of the pursuit game with partial information and characterizes graphs where the cat can guarantee a win, specifically forests.

Findings

Cat wins iff the graph is a forest

Partial distance info suffices for winning strategy

Extension of previous pursuit-evasion results

Abstract

We consider a variant of a pursuit and evasion game studied independently by Britnell and Wildon as well as Haslegrave. In their game, a cat has to catch an invisible mouse that moves along the edges of some graph $G$. In our version, the cat receives partial information about its distance to the mouse, and we show that the cat has a winning strategy if and only if $G$ is a forest. Seager proposed a similar game with complete distance information whose rules cause some small yet important differences to the game we consider.