Undirected Cat-and-Mouse is P-complete

TL;DR

This paper proves that the computational complexity of the cat-and-mouse game remains P-complete even on undirected graphs, extending previous results from directed graphs and providing new proofs.

Contribution

It establishes P-completeness of cat-and-mouse on undirected graphs and supplies a proof for the directed case, filling a gap in the literature.

Findings

Cat-and-mouse is P-complete on undirected graphs.

The paper provides a reduction from the circuit value problem.

It extends the known complexity results to undirected graphs.

Abstract

Cat-and-mouse is a two-player game on a finite graph. Chandra and Stockmeyer showed cat-and-mouse is P-complete on directed graphs. We show cat-and-mouse is P-complete on undirected graphs. To our knowledge, no proof of the directed case was ever published. To fill this gap we give a proof for directed graphs and extend it to undirected graphs. The proof is a reduction from a variant of the circuit value problem.