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arXiv · 2603.25365

Localization of the clique spectral version of Zykov's theorem

Changjiang Bu·Jueru Liu·Haotian Zeng
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Abstract

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.

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Changjiang Bu, Jueru Liu, Haotian Zeng. 2026-03-30. Localization of the clique spectral version of Zykov's theorem. https://arxiv.org/abs/2603.25365

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