General formulas for the instability minimum of Chip-firing games
Combinatorics
2026-04-16 v1
Abstract
In this article, we provide three formulas allowing to compute the minimum amount of initial chips leading to an infinite Chip-firing game. These formulas hold for strongly connected directed loop-free multigraphs and generalize what was already known in the Eulerian case. In addition to the many theoretical aspects, some algorithmic consequences are also investigated.
Cite
@article{arxiv.2604.13949,
title = {General formulas for the instability minimum of Chip-firing games},
author = {Merlin Michalski and Christophe Dubussy},
journal= {arXiv preprint arXiv:2604.13949},
year = {2026}
}
Comments
31 pages