P_3-Games

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.