由轮图导出的某些平面图类的星色数

The Star Chromatic Numbers of Some Planar Graphs Derived from Wheek

图的星色数是通常色数概念的推广.本文求出了几类由轮图导出的平面图的星色数.前两类是由3-或5-轮图经细分等构造出的,其星色数分别为2+2/(2n+1),2+3/(3n+1)和2+3/(3n-1).第三类平面图是由n-轮图经过Hajos构造得到的,其星色数为3+1/n.本类图的星色数结果推广了已有结论.

The notion of star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions, their star chromatic numbers being 2 + 2/(2n + 1), 2 + 3/(3n + 1) and 2 + 3/(3n - 1) separately. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of the result of Gao et al.