Planar graphs with maximum degree 8 and without intersecting chordal 4-cycles are 9-totally colorable  

作　　者：CAI JianSheng WANG GuangHui YAN GuiYing 

机构地区：[1]School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China [2]School of Mathematics, Shandong University, Jinan 250100, China [3]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science China Mathematics》2012年第12期2601-2612,共12页中国科学：数学（英文版）

基　　金：supported by Natural Science Foundation of Shandong Province (Grant No. ZR2009AM009);Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province (Grant No. BS2012SF016);National Natural Science Foundation of China (Grant Nos.11001055 and 11101243)

摘　　要：The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ″ （G）. It is shown that if a planar graph G has maximum degree Δ≥9, then χ″ （G） = Δ ＋ 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ″（G） = 9.

关 键 词：total coloring planar graph chordal 4-cycles TRIANGLES 

分 类 号：O157.5[理学—数学] O185.2[理学—基础数学]