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arXiv · 2606.04963

Localization of spectral Tur\'an theorems for signed graphs

Linfeng Xie·Xiaogang Liu
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Abstract

In this paper, we extend localized Tur\'an theorems to signed graphs and study the corresponding spectral Tur\'an problems. Firstly, we establish a vertex-localized Tur\'an-type inequality for signed graphs and characterize the extremal graphs reaching this bound. Secondly, we derive a sharp upper bound for the largest eigenvalue of a signed graph via localized Tur\'an parameters, and identify the extremal graphs attaining equality. Finally, we generalize a walk-based local spectral Tur\'an inequality to signed graphs. Our results generalize and improve several existing theorems for unsigned and signed graphs.

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Linfeng Xie, Xiaogang Liu. 2026-06-03. Localization of spectral Tur\'an theorems for signed graphs. https://arxiv.org/abs/2606.04963

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