最大度为5的可平面图是第一类的充分条件

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

最大度是5的可平面图,既有第一类,也有第二类。该文运用Discharge方法以及临界图的一些重要性质证明,每个最大度为5且不含三圈或不含四圈或不含五圈的简单平面图的边色数等于5,即这样的平面图是第一类的。文中还给出了最大度为5的平面图分类的一个特征刻画。

Both class 1 and class 2 planar graph exist in planar graphs with △≤5,where △ denotes the maximum degree of a planar graph.It is proved that the chromatic index of every simple planar graph G with △=5 and without 3-cycles or 4-cycles or 5-cycles is 5,i.e,such planar graphs to be class 1.