Impartial coloring games
Gabriel Beaulieu, Kyle Burke, Eric Duch\^ene

TL;DR
This paper explores six impartial coloring game variants, analyzing their outcome classes and computational complexity, with some focus on the Grundy function, expanding understanding of these combinatorial games.
Contribution
Introduces five new impartial coloring game rulesets derived from existing schemes and studies their outcome classes and complexity.
Findings
Outcome classes characterized for special cases
Computational complexity analyzed for each ruleset
Grundy function examined in certain cases
Abstract
Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial rulesets (five new), derived from previously-studied graph coloring schemes, including proper map coloring, oriented coloring, 2-distance coloring, weak coloring, and sequential coloring. For each, we study the outcome classes for special cases and general computational complexity. In some cases we pay special attention to the Grundy function.
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Taxonomy
TopicsArtificial Intelligence in Games · Digital Games and Media
