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arXiv · 2210.05867

Rainbow vertex pair-pancyclicity of strongly edge-colored graphs

Peixue Zhao·Fei Huang
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Abstract

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.

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Peixue Zhao, Fei Huang. 2022-10-12. Rainbow vertex pair-pancyclicity of strongly edge-colored graphs. https://doi.org/10.46298/dmtcs.10142

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