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Feedback arc set problem and NP-hardness of minimum recurrent configuration problem of Chip-firing game on directed graphs

In this paper we present further studies of recurrent configurations of Chip-firing games on Eulerian directed graphs (simple digraphs), a class on the way from undirected graphs to general directed graphs. A computational problem that arises naturally from this model is to find the minimum number of chips of a recurrent configuration, which we call the minimum recurrent configuration (MINREC) problem. We point out a close relationship between MINREC and the minimum feedback arc set (MINFAS) problem on Eulerian directed graphs, and prove that both problems are NP-hard.

preprint2013arXivOpen access
Kévin PerrotTrung Van Pham
math.COComputational ComplexityDiscrete Mathematics
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Kévin PerrotTrung Van Pham

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