Rainbow vertex pair-pancyclicity of strongly edge-colored graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914676303986688 |
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| author | Zhao, Peixue Huang, Fei |
| author_facet | Zhao, Peixue Huang, Fei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_05867 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rainbow vertex pair-pancyclicity of strongly edge-colored graphs Zhao, Peixue Huang, Fei Combinatorics 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. |
| title | Rainbow vertex pair-pancyclicity of strongly edge-colored graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2210.05867 |