List edge and list total coloring of 1-planar graphs  

作　　者：Xin ZHANG Jianliang WU Guizhen LIU 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Frontiers of Mathematics in China》2012年第5期1005-1018,共14页中国高等学校学术文摘·数学（英文）

摘　　要：A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that each 1-planar graph with maximum degree △ is （A ＋ 1）-edge-choosable and （△ ＋ 2）- total-choosable if △ ≥ 16, and is A-edge-choosable and （△ ＋ 1）-total-ehoosable if △ ≥21. The second conclusion confirms the list coloring conjecture for the class of 1-planar graphs with large maximum degree.A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that each 1-planar graph with maximum degree △ is （A ＋ 1）-edge-choosable and （△ ＋ 2）- total-choosable if △ ≥ 16, and is A-edge-choosable and （△ ＋ 1）-total-ehoosable if △ ≥21. The second conclusion confirms the list coloring conjecture for the class of 1-planar graphs with large maximum degree.

关 键 词：1-planar graph list coloring conjecture DISCHARGING 

分 类 号：O157.5[理学—数学] TP391.41[理学—基础数学]