P_3-Games
Wing-Kai Hon, Ton Kloks, Fu-Hong Liu, Hsiang-Hsuan Liu, Tao-Ming Wang

TL;DR
The paper introduces the P_3-game, demonstrating its decidability on various graph classes and establishing polynomial algorithms for the connected version on specific graph families.
Contribution
It proves the decidability of the P_3-game on elementary graphs and provides polynomial algorithms for the connected P_3-game on several complex graph classes.
Findings
Decidable for paths and cycles
Polynomial algorithms for connected P_3-game on trees, chordal graphs, ladders, cacti, outerplanar, and circular arc graphs
Advances understanding of P_3-game complexity on various graph classes
Abstract
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game is polynomially decidable for classes such as trees, chordal graphs, ladders, cacti, outerplanar graphs and circular arc graphs.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Artificial Intelligence in Games
