Chiraptophobic Cockroaches Evading a Torch Light

Abstract

We propose and study game-theoretic versions of independence
in graphs. The games are played by two players – the aggressor and the
defender – taking alternate moves on a graph G with tokens located on
vertices from an independent set of \(G\). A move of the aggressor is to select
a vertex v of \(G\). A move of the defender is to move tokens located on
vertices in \(N_G(v)\) each along one incident edge. The goal of the defender is
to maintain the set of occupied vertices independent while the goal of the
aggressor is to make this impossible. We consider the maximum number of
tokens for which the aggressor can not win in a strategic and an adaptive
version of the game.