论文标题
重新访问图形的半分边彩色
Revisiting Semistrong Edge-Coloring of Graphs
论文作者
论文摘要
如果$ m $的每个边缘在$ m $ $ m $引起的子图中，$ g $中匹配的$ m $是{\ em semistrong}。图$ g $的{\ em semistrong边缘色}是一个适当的边缘色，每个颜色类都可以诱导半符号匹配。在本文中，我们继续研究由Gyárfás和Hubenko发起的Semistrong边缘色的性质（{{semistrong graphs}。我们为通用图和最高度$ 3 $的图形建立了紧密的上限。我们还提出了有关半司令边彩的界限，这些界限来自其他有关其他无关的问题的结果。我们以几个开放的问题结束了论文。
A matching $M$ in a graph $G$ is {\em semistrong} if every edge of $M$ has an endvertex of degree one in the subgraph induced by the vertices of $M$. A {\em semistrong edge-coloring} of a graph $G$ is a proper edge-coloring in which every color class induces a semistrong matching. In this paper, we continue investigation of properties of semistrong edge-colorings initiated by Gyárfás and Hubenko ({Semistrong edge coloring of graphs}. \newblock {\em J. Graph Theory}, 49 (2005), 39--47). We establish tight upper bounds for general graphs and for graphs with maximum degree $3$. We also present bounds about semistrong edge-coloring which follow from results regarding other, at first sight non-related, problems. We conclude the paper with several open problems.
