The minimum edge-pancyclic graph of a given order
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909881271844864 |
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| author | Zhao, Xiamiao Yang, Yuxuan |
| author_facet | Zhao, Xiamiao Yang, Yuxuan |
| contents | A graph $G$ of order $n$ is called edge-pancyclic if, for every integer $k$ with $3 \leq k \leq n$, every edge of $G$ lies in a cycle of length $k$. Determining the minimum size $f(n)$ of a simple edge-pancyclic graph with $n$ vertices seems difficult. Recently, Li, Liu and Zhan \cite{li2024minimum} gave both a lower bound and an upper bound of $f(n)$. In this paper, we improve their lower bound by considering a new class of graphs and improve the upper bound by constructing a family of edge-pancyclic graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The minimum edge-pancyclic graph of a given order Zhao, Xiamiao Yang, Yuxuan Combinatorics A graph $G$ of order $n$ is called edge-pancyclic if, for every integer $k$ with $3 \leq k \leq n$, every edge of $G$ lies in a cycle of length $k$. Determining the minimum size $f(n)$ of a simple edge-pancyclic graph with $n$ vertices seems difficult. Recently, Li, Liu and Zhan \cite{li2024minimum} gave both a lower bound and an upper bound of $f(n)$. In this paper, we improve their lower bound by considering a new class of graphs and improve the upper bound by constructing a family of edge-pancyclic graphs. |
| title | The minimum edge-pancyclic graph of a given order |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.05506 |