Candy-passing Games on General Graphs, I

TL;DR

This paper introduces the first analysis of candy-passing games on arbitrary connected graphs, establishing a general stabilization result that extends previous findings on n-cycles with sufficient candies.

Contribution

It provides the first comprehensive study of candy-passing games on general graphs and proves a stabilization result that generalizes earlier specific cases.

Findings

Established a stabilization result for candy-passing games on connected graphs.

Extended previous results from n-cycles to arbitrary connected graphs.

Demonstrated conditions for game stabilization based on total candies.

Abstract

We undertake the first study of the candy-passing game on arbitrary connected graphs. We obtain a general stabilization result which encompasses the first author's results (arXiv:0709.2156) for candy-passing games on n-cycles with at least 3n candies.