三角形六角系统的星边色数

Star Chromatic Index of Triangle-Shaped Polyhexes

图G的一个边染色称作是G的正常边染色,如果G中任意两条邻接边上所染颜色不同.如果图G的一个正常边染色使得G中没有长为4的路或4-圈是2-边染色的,则称此边染色是G的一个星边染色.对G进行星边染色所需的最小颜色数称为G的星边色数.研究了三角形六角系统的星边染色,应用构造方法证明了三角形六角系统的星边色数等于4.

An edge-coloring of a graph G is called a proper edge-coloring of G if any two adjacent edges do not have the same color. A proper edge-coloring of graph G is called a star edge-coloring of G if there is neither 2-edge colored path with length four nor 2-edge colored cycle with length four in G. The minimum number of colors required for any star edge-coloring of G is called the star chromatic index of G. By using constructive method, it is proved that the star chromatic index of triangle-shaped polyhexes is four