Abstract
A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v ∈ V(G)} with ∣L(v)∣ ≥ k for each vertex v ∈ V(G), there exists an acyclic proper vertex coloring ϕ of G such that ϕ(v) ∈ L(v) for each vertex v ∈ V(G). In this paper, we prove that every graph G embedded on the surface with Euler characteristic number ε = −1 is acyclically 11-choosable.
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Supported by NSFC (Grant Nos. 12101285, 12171222), Basic and Applied Basic Research Foundation and Joint Foundation Project of Guangdong Province, China (Grant No. 2019A1515110324), Guangdong Basic and Applied Basic Research Foundation (Natural Science Foundation of Guangdong Province, China, Grant No. 2021A1515010254), Foundation of Lingnan Normal University (Grant Nos. ZL2021017, ZL1923)
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Sun, L., Yu, G.L. & Li, X. Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable. Acta. Math. Sin.-English Ser. 39, 2247–2258 (2023). https://doi.org/10.1007/s10114-023-1518-y
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DOI: https://doi.org/10.1007/s10114-023-1518-y