Paintbucket on graphs is PSPACE-complete

TL;DR

This paper proves that determining the winner in a generalized version of the game Paintbucket on arbitrary graphs is PSPACE-complete, highlighting its computational complexity.

Contribution

It introduces a generalized version of Paintbucket on graphs and establishes its PSPACE-completeness, a novel complexity result for this class of games.

Findings

Determined the computational complexity of generalized Paintbucket as PSPACE-complete.

Extended the game analysis from grids to arbitrary graphs.

Provided complexity-theoretic insights into game strategy determination.

Abstract

The game of Paintbucket was recently introduced by Amundsen and Erickson. It is played on a rectangular grid of black and white pixels. The players alternately fill in one of their opponent's connected components with their own color, until the entire board is just a single color. The player who makes the last move wins. It is not currently known whether there is a simple winning strategy for Paintbucket. In this paper, we consider a natural generalization of Paintbucket that is played on an arbitrary simple graph, and we show that the problem of determining the winner in a given position of this generalized game is PSPACE-complete.