平面图的强边染色

图$G$的强边染色是在正常边染色的基础上, 要求距离不超过$2$的任意两条边染不同的颜色, 强边染色所用颜色的最小整数称为图$G$的强边色数。本文首先给出极小反例的构型, 然后通过权转移法, 证明了$g(G)geq5$, $Delta(G)geq6$且$5$-圈不相交的平面图的强边色数至多是$4Delta(G)-1$。

Strong edge-coloring of planar graphs

A strong edge coloring of graph $G$ is on the basis of the proper edge coloring and requiring any two edges at distance at most 2 receive distinct colors, the smallest integer of strong edge coloring called a figure of colors used strong edge chromatic number of $G$. In this paper, the configuration of the minimal counter example is given, and then the power transfer method is used to prove that the strong chromatic index of plane graphs with $g(G)geq5$, $Delta(G)geq6$ and $5$-cycle do not intersect is at most $4Delta(G)-1$.