Complexity of the Game Domination Problem
Bo\v{s}tjan Bre\v{s}ar, Paul Dorbec, Sandi Klav\v{z}ar, Ga\v{s}per, Ko\v{s}mrlj, Gabriel Renault
TL;DR
This paper proves that determining whether the game domination number of a graph is bounded by a given integer is a PSPACE-complete problem, highlighting its computational complexity.
Contribution
It establishes the PSPACE-completeness of the game domination number problem, a significant complexity result in graph theory and combinatorial game analysis.
Findings
Verifying the boundedness of the game domination number is PSPACE-complete.
Contrasts with the unknown complexity of the game coloring problem.
Provides a complexity classification for a graph invariant related to a combinatorial game.
Abstract
The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game domination number of a graph is bounded by a given integer is PSPACE-complete. This contrasts the situation of the game coloring problem whose complexity is still unknown.
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