We give a new proof that any candy-passing game on a graph G with at least 4|E(G)| − |V (G)| candies stabilizes. Unlike the prior literature on candy-passing games, we use methods from the general theory of chip-firing games which allow us to obtain a polynomial bound on the number of rounds before stabilization.
We let G be an undirected graph and denote the vertex and edge sets of G by V (G) and E(G), respectively. The candy-passing game on G is defined by the following rules: • At the beginning of the game, c > 0 candies are distributed among |V (G)| students, each of whom is seated at some distinct vertex v ∈ V (G). • A whistle is sounded at a regular interval.… (More)