Network control games played on graphs

Abstract

We study network-control games played on graphs. These games belong to the class of scoring games in combinatorial game theory. In a network-control game, two players alternate in rounds on a given graph. During each round, a player selects an unclaimed vertex with its unclaimed neighbours within the distance t. The objective is to decide which player can claim more vertices at the end of the play. We study network-control games on various classes of graphs, including paths, linear forests, and hub-and-spoke graphs. Additionally, we examine greedy, symmetric, and optimal strategies. In the context of scoring games, concepts and techniques developed in this paper contribute to the further understanding and development of combinatorial game theory.