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Acyclic 6-choosability of Planar Graphs without 5-cycles and Adjacent 4-cycles
Acta Mathematica Sinica, English Series ( IF 0.7 ) Pub Date : 2021-06-15 , DOI: 10.1007/s10114-021-9335-7 Lin Sun
中文翻译:
无 5 环和相邻 4 环的平面图的非循环 6 可选取性
更新日期:2021-06-21
Acta Mathematica Sinica, English Series ( IF 0.7 ) Pub Date : 2021-06-15 , DOI: 10.1007/s10114-021-9335-7 Lin Sun
A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v ∈ V(G)} with ∣L(v)∣ ≥ k for all v ∈ V(G), there exists a proper acyclic vertex coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V(G). In this paper, we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles, then G is acyclically 6-choosable.
中文翻译:
无 5 环和相邻 4 环的平面图的非循环 6 可选取性
如果每个循环至少使用三种颜色,则图的正确顶点着色是非循环的。如果对于任何列表分配L = { L ( v ): v ∈ V ( G )} 且对于所有v ∈ V ( G ) ∣ L ( v )∣ ≥ k,则图G是非循环k-choosable 的,存在一个适当的对G 的无环顶点着色φ,使得 φ( v ) ∈ L ( v ) 对于所有v ∈ V (格)。在本文中,我们证明了如果G是一个平面图并且不包含 5 个圈且不包含相邻的 4 个圈,则G是非循环 6 可选的。