最大度为6不含相邻弦6-圈的平面图的全染色

Total Colorings of Planar Graphs with Maximum Degree 6 and without Adjacent Chordal 6-Cycles

图的全染色是指对图的顶点和边进行染色,使得相邻或相关联的元素染不同的颜色.利用权转移方法,证明了最大度为6且不含相邻弦6-圈的简单平面图是8-全可染的.该结果是对全染色猜想的进一步支持.

Total coloring of a graph is to color the vertices and edges such that no incident or adjacent elements receive the same color.In this paper,we use discharging method to verify that every simple planar graph with maximum degree 6 and without adjacent chordal 6-cycles is 8-totally-colorable.This result gives further affirmative support to Total Coloring Conjecture.