标题：The adjacent vertex distinguishing total choosability of planar graphs with maximum degree at least eleven
作者：Cheng, Xiaohan; Wu, Jianliang
作者机构：[Cheng, Xiaohan] Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China.; [Wu, Jianliang] Shandong Univ, Sch Math, Jinan 250100, Shandong 更多
通讯作者地址：[Wu, JL]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：JOURNAL OF COMBINATORIAL OPTIMIZATION
关键词：Adjacent vertex distinguishing total choosability; Planar graph; Maximum; degree
摘要：A (proper) total-k-coloring of a graph G is a mapping such that any two adjacent or incident elements in receive different colors. Let C(v) denote the set of the color of a vertex v and the colors of all incident edges of v. An adjacent vertex distinguishing total-k-coloring of G is a total-k-coloring of G such that for each edge , . We denote the smallest value k in such a coloring of G by . It is known that for any planar graph with . In this paper, we consider the list version of this coloring and show that if G is a planar graph with , then , where is the adjacent vertex distinguishing total choosability.