科研之友
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摘要
A list assignment of a graph G is a function L that assigns a list L(v) of colors to each vertex . An -coloring is a mapping that assigns a color to each vertex so that at most d neighbors of v receive color . A graph G is said to be -choosable if it admits an -coloring for every list assignment L with for all . In this paper, we prove that every planar graph with neither adjacent triangles nor 6-cycles is -choosable. This is a partial answer to a question of Xu and Zhang (Discret Appl Math 155:74-78, 2007) that every planar graph without adjacent triangles is -choosable. Also, this improves a result in Lih et al. (Appl Math Lett 14:269-273, 2001) which says that every planar graph without 4- and 6-cycles is -choosable.
- 出版日期2016-10
- 单位浙江师范大学
