Spectral radius and Hamiltonicity of uniform hypergraphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908955710586880 |
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| author | Brooks, George Linz, William Luo, Ruth |
| author_facet | Brooks, George Linz, William Luo, Ruth |
| contents | Let $n$ and $r$ be integers with $n-2\ge r\ge 3$. We prove that any $r$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with spectral radius $λ(\mathcal{H}) > \binom{n-2}{r-1}$ must contain a Hamiltonian Berge cycle unless $\mathcal{H}$ is the complete graph $K_{n-1}^r$ with one additional edge. This generalizes a result proved by Fiedler and Nikiforov for graphs. As part of our proof, we show that if $|\mathcal{H}| > \binom{n-1}{r}$, then $\mathcal{H}$ contains a Hamiltonian Berge cycle unless $\mathcal{H}$ is the complete graph $K_{n-1}^r$ with one additional edge, generalizing a classical theorem for graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral radius and Hamiltonicity of uniform hypergraphs Brooks, George Linz, William Luo, Ruth Combinatorics Let $n$ and $r$ be integers with $n-2\ge r\ge 3$. We prove that any $r$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with spectral radius $λ(\mathcal{H}) > \binom{n-2}{r-1}$ must contain a Hamiltonian Berge cycle unless $\mathcal{H}$ is the complete graph $K_{n-1}^r$ with one additional edge. This generalizes a result proved by Fiedler and Nikiforov for graphs. As part of our proof, we show that if $|\mathcal{H}| > \binom{n-1}{r}$, then $\mathcal{H}$ contains a Hamiltonian Berge cycle unless $\mathcal{H}$ is the complete graph $K_{n-1}^r$ with one additional edge, generalizing a classical theorem for graphs. |
| title | Spectral radius and Hamiltonicity of uniform hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.18314 |