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• W3037947434 abstract "We suggest a measure of “Eulerianness” of a finite directed graph and define a class of “coEulerian” graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we address a question in chip-firing posed by Björner, Lovász, and Shor in 1991, who asked for “<italic>a characterization of those digraphs and initial chip configurations that guarantee finite termination.</italic>” Björner and Lovász gave an exponential time algorithm in 1992. We show that this can be improved to linear time if the graph is coEulerian, and that the problem is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sans-serif NP> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext mathvariant=sans-serif>NP</mml:mtext> </mml:mrow> <mml:annotation encoding=application/x-tex>textsf {NP}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-complete for general directed multigraphs." @default.
• W3037947434 created "2020-07-02" @default.
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• W3037947434 date "2015-12-21" @default.
• W3037947434 modified "2023-10-14" @default.
• W3037947434 title "CoEulerian graphs" @default.
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• W3037947434 doi "https://doi.org/10.1090/proc/12952" @default.
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