List Total Colorings of Planar Graphs without Triangles at Small Distance  

作　　者：Bin LIU Jian Feng HOU Gui Zhen LIU 

机构地区：[1]Department of Mathematics, Ocean University of China, Qingdao 266100, P. R. China [2]Center for Discrete Mathematics, Fuzhou University, Fuzhou 350002, P. R. China [3]School of Mathematics, Shandong University, Ji＇nan 250100, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第12期2437-2444,共8页数学学报（英文版）

摘　　要：Suppose that G is a planar graph with maximum degree △. In this paper it is proved that G is total-（△ ＋ 2）-choosable if （1） △ ≥ 7 and G has no adjacent triangles （i.e., no two triangles are incident with a common edge）; or （2） △ ≥6 and G has no intersecting triangles （i.e., no two triangles are incident with a common vertex）; or （3） △ ≥ 5, G has no adjacent triangles and G has no k-cycles for some integer k ∈ {5, 6}.Suppose that G is a planar graph with maximum degree △. In this paper it is proved that G is total-（△ ＋ 2）-choosable if （1） △ ≥ 7 and G has no adjacent triangles （i.e., no two triangles are incident with a common edge）; or （2） △ ≥6 and G has no intersecting triangles （i.e., no two triangles are incident with a common vertex）; or （3） △ ≥ 5, G has no adjacent triangles and G has no k-cycles for some integer k ∈ {5, 6}.

关 键 词：List total coloring CHOOSABILITY planar graph 

分 类 号：O123.1[理学—数学] TP391.41[理学—基础数学]