关于Halin图的边面全着色数

The Edge-Face Total Chromatic Number of Halin Graphs

设Ｘｃ（Ｇ）在示Ｈａｌｉｎ图Ｇ的边面全色数。文献［１］中提出如下两个猜想：（１）对△（Ｇ）＝３的Ｈａｌｉｎ图Ｇ，有４≤ＸｃＡ（Ｇ）≤５；（２）对△（Ｇ）＝６的Ｈａｌｉｎ图Ｇ。有Ｘｃ（Ｇ）＝６．其中△（Ｇ）表示图Ｇ的最大度数。本文证明了这两个猜想的正确性。

Let X(G)be the edge-face total chromatic number of a Halin graph G.In paper[1],two conjectures are proposed as follows:(1)If G is a Halin Graph,and △(G)=3,then 4≤Xe(G)≤5;(2)If G is a Halin Graph,and△(G)=6, then Xe(G)=6,where△(G)denotes the maximum degree of G. In this paper,that conjectures(1)and(2)are true is proved.