Localization of the clique spectral version of Zykov's theorem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914431291621376 |
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| author | Bu, Changjiang Liu, Jueru Zeng, Haotian |
| author_facet | Bu, Changjiang Liu, Jueru Zeng, Haotian |
| contents | Zykov's theorem shows that $r$-partite Turán graph uniquely has the maximum number of $K_t$ among all $n$-vertex $K_{r+1}$-free graphs for $2\le t\le r$. The clique tensor is a high-order extension of the adjacency matrix of a graph. Yu and Peng \cite{peng1} gave a spectral version of the Zykov's theorem via clique tensor. In this paper, we give some upper bounds on the spectral radius of the clique tensor of a graph, which can be viewed as the localizations of the spectral version of Zykov's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25365 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localization of the clique spectral version of Zykov's theorem Bu, Changjiang Liu, Jueru Zeng, Haotian Combinatorics Zykov's theorem shows that $r$-partite Turán graph uniquely has the maximum number of $K_t$ among all $n$-vertex $K_{r+1}$-free graphs for $2\le t\le r$. The clique tensor is a high-order extension of the adjacency matrix of a graph. Yu and Peng \cite{peng1} gave a spectral version of the Zykov's theorem via clique tensor. In this paper, we give some upper bounds on the spectral radius of the clique tensor of a graph, which can be viewed as the localizations of the spectral version of Zykov's theorem. |
| title | Localization of the clique spectral version of Zykov's theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.25365 |