Conflicting chip firing games on graphs and on trees

Abstract

Chip Firing Games on (directed) graph are widely used in theoretical computer science and many other sciences. In this model, chips are fired from one vertex to all of its neighbors at the same time. The purpose of our paper is to study an extended version of this model, the Conflicting Chip Firing Game, by considering that chips can be fired from one vertex to one of its neighbors at each time. Our main results are obtained when the support graph of this game is a rooted tree. In this case, we give the characterization of its reachable configurations and of its fixed points. Moreover we show the local lattice structure of its configuration space.