Keeping Your Distance is Hard

TL;DR

This paper investigates the computational complexity of a broad class of distance games played on graphs, establishing that many are PSPACE-hard, thus highlighting their computational difficulty.

Contribution

It extends the complexity analysis to many more distance games beyond well-known examples, proving their PSPACE-hardness.

Findings

Many distance games are PSPACE-hard.

Complexity results apply to a wide range of distance games.

The study broadens understanding of the computational difficulty of graph-based games.

Abstract

We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is the set of forbidden distances for colouring vertices in different colors, while S is the set of forbidden distances for the same colour. The last player to move wins. Well-known examples of distance games are Node-Kayles, Snort, and Col, whose complexities were shown to be PSPACE-hard. We show that many more distance games are also PSPACE-hard.