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(3,1)*-choosability of plane graphs without adjacent single cycles
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Given a list assignment of L to graph G,assign a list L(v)of colors to each v∈V(G).An(L,d)*-coloring is a mapping π that assigns a colorπ(v)∈ L(v)to each vertex v ∈ V(G)such that at most d neighbors of v receive the color v.If there exists an(L,d)*-coloring for every list assignment L with|L(v)|≥k for all v ∈ V(G),then G is called to be(k,d)*-choosable.In this paper,we prove every planar graph G without adjacent k-cycles is(3,1)*-choos-able,where k ∈ {3,4,5}.
Plane graphimproper list coloring(kd)*-choosablecycle
Jufeng ZHANG、Min CHEN、Yiqiao WANG
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College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China
School of Management,Beijing University of Chinese Medicine,Beijing 100029,China
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