Rank-determining sets of metric graphs
Journal of Combinatorial Theory Series A
Chip-firing games, potential theory on graphs, and spanning trees
Journal of Combinatorial Theory Series A
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We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit, allowing us to treat the greedy reduction algorithm as a transfinite algorithm and to analyze its running time via ordinal numbers. Matching lower and upper bounds on worst case running time of O(@w^n) are provided.