最大度为6且不含5圈或6圈的平面图可8全染色

G,G的k 全染色是指用k种颜色给G的点和边进行染色,使G的任意邻接点或邻接边均染不同的颜色,且G的任一点与该点的任一关联边均染不同的颜色．证明了最大度为6且不含5 圈或6 圈的平面图是可8 全染色的．

Every planar graph with maximum degree 6 and without 5-cycle or 6-cycle is totally 8-colorable

Given a graph G, a total k-coloring of G is a coloring of the vertices and edges of G with k colors, such that no two adjacent vertices or edges have the same color; The color of each vertex is distinct from the colors of its incident edges. It is proved that if a planar graph has the maximum degree and has no 5-cycle or 6-cylcle, then it can be totally 8-colorable.