最大度是6的平面图是第一类图的一个充分条件

A sufficient condition for a planar graph of maximum degree six to be class 1

用χ′(G)表示G的边染色数.对于最大度是Δ的可平面图G,如果χ′(G)=Δ,称G为第一类图;如果χ′(G)=Δ+1,称G为第二类图.运用Discharge方法证明:最大度是6且不含7圈的可平面图G是第一类图.

Let G be a planar graph of maximum degree Δ,G is said to be class 1 if χ′（G）=Δ and class 2 if χ′（G）=Δ＋1,where χ′（G） denotes the chromatic index of G.By applying a discharging method,it is proved that every simple planar graph G with Δ=6 is of class 1,if G contains no any 7-cycle.