论文标题
彩虹顶点对强度的图形
Rainbow vertex pair-pancyclicity of strongly edge-colored graphs
论文作者
论文摘要
如果图形的两个边缘没有相同的颜色，则边缘色图为\ emph {Rainbow}。如果每两个相邻的边缘的$ g^c $的每两个边缘在$ g^c $中获得不同的颜色，则称为\ emph {正确彩色}，称为\ emph {正确的颜色。 \ emph {强边彩}图是一个正确的边缘色图，因此每一个长度的路径$ 3 $都是彩虹。如果$ g^c $中的任何两个顶点包含在$ g^c $中的任何两个顶点，则我们称为边缘色的图$ g^c $ \ emph {Rainbow顶点成对 - 庞然大物}，每个$ \ ell $ in $ g^c $中的任何两个顶点都包含在$ \ ell $中，$ \ ell $，带有$ 3 \ leq \ leq \ leq \ ell \ ell \ ell \ leq n $。在本文中，我们表明，每个强烈边缘的图形$ g^c $ of订单$ n $，带有最低度$δ\ geq \ geq \ frac {2n} {3} {3} {3}+1 $ is rainbow pertex pairtex papy-pancyclicity。
An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$. A \emph{strongly edge-colored} graph is a proper edge-colored graph such that every path of length $3$ is rainbow. We call an edge-colored graph $G^c$ \emph{rainbow vertex pair-pancyclic} if any two vertices in $G^c$ are contained in a rainbow cycle of length $\ell$ for each $\ell$ with $3 \leq \ell \leq n$. In this paper, we show that every strongly edge-colored graph $G^c$ of order $n$ with minimum degree $δ\geq \frac{2n}{3}+1$ is rainbow vertex pair-pancyclicity.
