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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The first author is supported by National Natural Science Foundation of China (Grant No. 11001055) and Natural Science Foundation of Fujian Province (Grant Nos. 2010J05004 and 2011J06001); the second author is supported by National Natural Science Foundation of China (Grant No. 60672030)
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Hou, J.F., Liu, G.Z. Every toroidal graph is acyclically 8-choosable. Acta. Math. Sin.-English Ser. 30, 343–352 (2014). https://doi.org/10.1007/s10114-013-1497-5
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DOI: https://doi.org/10.1007/s10114-013-1497-5