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- W4282922384 abstract "It's well known that every planar graph is $4$-colorable. A toroidal graph is a graph that can be embedded on a torus. It's proved that every toroidal graph is $7$-colorable. A proper coloring of a graph is called emph{odd} if every non-isolated vertex has at least one color that appears an odd number of times in its neighborhood. The smallest number of colors that admits an odd coloring of a graph $ G $ is denoted by $chi_{o}(G)$. In this paper, we prove that if $G$ is tortoidal, then $chi_{o}left({G}right)le9$; Note that $K_7$ is a toroidal graph, the upper bound is no less than $7$." @default.
- W4282922384 created "2022-06-16" @default.
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- W4282922384 date "2022-06-12" @default.
- W4282922384 modified "2023-09-30" @default.
- W4282922384 title "The odd chromatic number of a toroidal graph is at most 9" @default.
- W4282922384 doi "https://doi.org/10.48550/arxiv.2206.05780" @default.
- W4282922384 hasPublicationYear "2022" @default.
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