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- W4294328963 abstract "Given an undirected graph $G=(V,E)$, and a designated vertex $qin V$, the notion of a $G$-parking function (with respect to $q$) was independently developed and studied by various authors, and has recently gained renewed attention. This notion generalizes the classical notion of a parking function associated with the complete graph. In this work, we study properties of {em maximum} $G$-parking functions and provide a new bijection between them and the set of spanning trees of $G$ with no broken circuit. As a case study, we specialize some of our results to the graph corresponding to the discrete $n$-cube $Q_n$. We present the article in an expository self-contained form, since we found the combinatorial aspects of $G$-parking functions somewhat scattered in the literature, typically treated in conjunction with sandpile models and closely related chip-firing games." @default.
- W4294328963 created "2022-09-02" @default.
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- W4294328963 date "2008-01-07" @default.
- W4294328963 modified "2023-09-26" @default.
- W4294328963 title "$G$-Parking Functions, Acyclic Orientations and Spanning Trees" @default.
- W4294328963 doi "https://doi.org/10.48550/arxiv.0801.1114" @default.
- W4294328963 hasPublicationYear "2008" @default.
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