Cops and Robbers is EXPTIME-complete

TL;DR

This paper proves that determining whether k cops can catch a robber on a graph is EXPTIME-complete, confirming a long-standing conjecture and highlighting the problem's computational difficulty.

Contribution

The paper establishes the EXPTIME-completeness of the cops and robbers problem when both the graph and the number of cops are input parameters.

Findings

The problem is proven to be EXPTIME-complete.

Confirms the conjecture by Goldstein and Reingold from 1995.

Highlights the computational complexity of pursuit-evasion games on graphs.

Abstract

We investigate the computational complexity of deciding whether k cops can capture a robber on a graph G. In 1995, Goldstein and Reingold conjectured that the problem is EXPTIME-complete when both G and k are part of the input; we prove this conjecture.