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arXiv · 2610.21388

Stronger Spectral Bound for Clique Number

Hareshkumar Jadav·Sudipta Mallik·Akhilesh Panchangam·Ranveer Singh
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Abstract

Given an integer $k$, deciding whether a graph has a clique of size $k$ is an NP-complete problem. Wilf's inequality provides a spectral lower bound for the clique number of a graph. Strengthening this bound, Elphick and Wocjan proposed a conjecture in 2018 using positive adjacency eigenvalues. In this paper, we present an infinite family of graphs for which the Elphick and Wocjan conjecture is true. We find a stronger spectral lower bound for the clique number for this family of graphs.

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Hareshkumar Jadav, Sudipta Mallik, Akhilesh Panchangam, Ranveer Singh. 2026-10-15. Stronger Spectral Bound for Clique Number. https://arxiv.org/abs/2610.21388

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