Ordinary and spectral extremal problems on vertex disjoint copies of even fans
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918025061466112 |
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| author | Cai, Yiting Zhou, Bo |
| author_facet | Cai, Yiting Zhou, Bo |
| contents | Let $\mathrm{ex}(n, F)$ and $\mathrm{spex}(n, F)$ be the maximum size and spectral radius among all $F$-free graphs with fixed order $n$, respectively. A fan is a graph $P_1\vee P_{s}$ (join of a vertex and a path of order $s$) for $s\ge 3$, and it is called an even fan if $s$ is even. In this paper, we study $\mathrm{ex}(n,t(P_1\vee P_{2k}))$, $\mathrm{spex}(n,t(P_1\vee P_{2k}))$ with $t\ge 1$ and $k\ge 3$ and characterize the corresponding extremal graphs for sufficiently large $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ordinary and spectral extremal problems on vertex disjoint copies of even fans Cai, Yiting Zhou, Bo Combinatorics Let $\mathrm{ex}(n, F)$ and $\mathrm{spex}(n, F)$ be the maximum size and spectral radius among all $F$-free graphs with fixed order $n$, respectively. A fan is a graph $P_1\vee P_{s}$ (join of a vertex and a path of order $s$) for $s\ge 3$, and it is called an even fan if $s$ is even. In this paper, we study $\mathrm{ex}(n,t(P_1\vee P_{2k}))$, $\mathrm{spex}(n,t(P_1\vee P_{2k}))$ with $t\ge 1$ and $k\ge 3$ and characterize the corresponding extremal graphs for sufficiently large $n$. |
| title | Ordinary and spectral extremal problems on vertex disjoint copies of even fans |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.09183 |