Every toroidal graph is acyclically 8-choosable |
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Authors: | Jian Feng Hou Gui Zhen Liu |
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Institution: | 1. Center for Discrete Mathematics, Fuzhou University, Fujian, 350002, P. R. China 2. School of Mathematics, Shandong University, Ji’nan, 250100, P. R. China
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Abstract: | A proper coloring of a graph G is acyclic if G contains no 2-colored cycle. A graph G is acyclically L-list colorable if for a given list assignment L = {L(v): v ∈ V (G)}, there exists a proper acyclic coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V (G). If G is acyclically L-list colorable for any list assignment L with |L(v)| ≥ k for all v ∈ V (G), then G is acyclically k-choosable. In this article, we prove that every toroidal graph is acyclically 8-choosable. |
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Keywords: | Acyclic coloring choosability toroidal graph |
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