A faster algorithm for Cops and Robbers

TL;DR

This paper introduces a more efficient algorithm with time complexity $O(kn^{k+2})$ for determining if a graph is $k$-copwin, improving upon the previous $O(n^{2k+2})$ algorithm.

Contribution

The paper presents a faster algorithm for the Cops and Robbers problem, reducing the computational complexity for deciding $k$-copwin graphs.

Findings

New algorithm with $O(kn^{k+2})$ complexity

Significant speed-up over previous methods

Applicable to graphs with large vertex counts

Abstract

We present an algorithm of time complexity $O(kn^{k+2})$ deciding whether a graph $G$ on $n$ vertices is $k$-copwin. The fastest algorithm thus far had time complexity $O(n^{2k+2})$.