Geodesic
Rainbow vertex pair-pancyclicity of strongly edge-colored graphs
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1.

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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.
DOI : 10.46298/dmtcs.10142
Classification : 05C15, 05C38 
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Zhao, Peixue; Huang, Fei. Rainbow vertex pair-pancyclicity of strongly edge-colored graphs. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1. doi : 10.46298/dmtcs.10142. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.10142/

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