Chip-firing games on Eulerian digraphs and NP-hardness of computing the rank of a divisor on a graph

Viktor Kiss; Lilla Tóthmérész

doi:10.1016/j.dam.2015.04.030

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arXiv · 1407.6958

Chip-firing games on Eulerian digraphs and NP-hardness of computing the rank of a divisor on a graph

Viktor Kiss·Lilla Tóthmérész

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Abstract

Baker and Norine introduced a graph-theoretic analogue of the Riemann-Roch theory. A central notion in this theory is the rank of a divisor. In this paper we prove that computing the rank of a divisor on a graph is NP-hard. The determination of the rank of a divisor can be translated to a question about a chip-firing game on the same underlying graph. We prove the NP-hardness of this question by relating chip-firing on directed and undirected graphs.

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Viktor Kiss, Lilla Tóthmérész. 2014-07-25. Chip-firing games on Eulerian digraphs and NP-hardness of computing the rank of a divisor on a graph. https://doi.org/10.1016/j.dam.2015.04.030

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