Peixue Zhao ; Fei Huang - Rainbow vertex pair-pancyclicity of strongly edge-colored graphs

dmtcs:10142 - Discrete Mathematics & Theoretical Computer Science, May 16, 2023, vol. 25:1 -
Rainbow vertex pair-pancyclicity of strongly edge-colored graphs

Authors: Peixue Zhao ; Fei Huang

    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 $\delta \geq \frac{2n}{3}+1$ is rainbow vertex pair-pancyclicity.

    Volume: vol. 25:1
    Section: Graph Theory
    Published on: May 16, 2023
    Accepted on: April 1, 2023
    Submitted on: October 13, 2022
    Keywords: Mathematics - Combinatorics

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