Algorithms for Chip-Firing on Weighted Graphs

Published 31 Oct 2023 in math.CO | (2311.00194v1)

Abstract: We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent $q$-reduced divisors. Finally, we illustrate a method of finding all maximal unwinnable divisors on weighted graphs.

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Ben Doyle

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