Halin图的一个点强全染色法

Method on vertex strong total coloring of Halin graphs

针对Halin图的点强全染色问题,提出一个有效的染色法———逐圈着色法,而且方法给出的方案也是最优的,即用最少的颜色完成Halin图的点强全染色.同时还确定了最大顶点度是3的Halin图的点强全色数的上下界,即上界为6,下界为5.

An effective coloring method was given on the problem of vertex strong total coloring of Halin Graphs constructively-the method of coloring cycles one by one is proposed, which is evaluated as the best one. Namely, using the least number of colors, it is possible to finish the vertex strong total coloring of Halin Graphs. Meanwhile, the bounds of the vertex strong total chromatic number of Halin graphs with maximum degree 3 were given. The upper bound and the lower bound are 6 and 5, respectively.