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- W4380375413 abstract "We study a version of the lights out game played on directed graphs. For a digraph $D$, we begin with a labeling of $V(D)$ with elements of $mathbb{Z}_k$ for $k ge 2$. When a vertex $v$ is toggled, the labels of $v$ and any vertex that $v$ dominates are increased by 1 mod $k$. The game is won when each vertex has label 0. We say that $D$ is $k$-Always Winnable (also written $k$-AW) if the game can be won for every initial labeling with elements of $mathbb{Z}_k$. We prove that all acyclic digraphs are $k$-AW for all $k$, and we reduce the problem of determining whether a graph is $k$-AW to the case of strongly connected digraphs. We then determine winnability for tournaments with a minimum feedback arc set that arc-induces a directed path or directed star digraph." @default.
- W4380375413 created "2023-06-13" @default.
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- W4380375413 date "2023-06-09" @default.
- W4380375413 modified "2023-09-27" @default.
- W4380375413 title "The Lights Out Game on Directed Graphs" @default.
- W4380375413 doi "https://doi.org/10.48550/arxiv.2306.06017" @default.
- W4380375413 hasPublicationYear "2023" @default.
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