标题：Minimum choosability of planar graphs
作者：Wang, Huijuan; Liu, Bin; Gai, Ling; Du, Hongwei; Wu, Jianliang
作者机构：[Wang, Huijuan] Qingdao Univ, Sch Math & Stat, Qingdao 266100, Peoples R China.; [Liu, Bin] Ocean Univ China, Dept Math, Qingdao 266100, Peoples R C 更多
通讯作者：Gai, L;Gai, Ling
通讯作者地址：[Gai, L]Shanghai Univ, Sch Management, Shanghai 201444, Peoples R China.
来源：JOURNAL OF COMBINATORIAL OPTIMIZATION
关键词：List coloring; Choosability; Planar graph; Chordal
摘要：The problem of list coloring of graphs appears in practical problems concerning channel or frequency assignment. In this paper, we study the minimum number of choosability of planar graphs. A graph G is edge-k-choosable if whenever every edge x is assigned with a list of at least k colors, L(x)), there exists an edge coloring such that . Similarly, A graph G is toal-k-choosable if when every element (edge or vertex) x is assigned with a list of at least k colors, L(x), there exists an total coloring such that . We proved and for a planar graph G with maximum degree and without chordal 6-cycles, where the list edge chromatic number of G is the smallest integer k such that G is edge-k-choosable and the list total chromatic number of G is the smallest integer k such that G is total-k-choosable.