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On r-hued list coloring of K4(7)-minor free graphs
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NSTL
Elsevier
? 2021 Elsevier B.V.For a given list assignment L of a graph G, an (L,r)-coloring of G is a proper coloring c such that for any vertex v with degree d(v), v is adjacent to vertices of at least min{d(v),r} different color with c(v)∈L(v). The r-hued list chromatic number of G, denoted as χL,r(G), is the least integer k, such that for any v∈V(G) and every list assignment L with |L(v)|=k, G has an (L,r)-coloring. Let K(r)=r+3 if 2≤r≤3, K(r)=?3r/2?+1 if r≥4. In Song et al. (2014), it is proved that if G is a K4-minor-free graph, then χL,r(G)≤K(r)+1. Let K4(n) be the set of all subdivisions of K4 on n vertices. Utilizing the decompositions by Chen et al for K4(7)-minor free graphs in Chen et al. (2020), we prove that if G is a K4(7)-minor free graph, then χL,r(G)≤K(r)+1.
(Lr)-coloringGraph minorr-hued list chromatic number
Wei W.、Liu F.、Xiong W.、Lai H.-J.
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College of Mathematics and System Sciences Xinjiang University Urumqi
Department of Mathematics West Virginia University
NSTL
Elsevier
