Hypergraph independence polynomials with a zero close to the origin

2023/05/28 by Shengtong Zhang, Zhang, Shengtong · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2305.17822

Abstract

For each uniformity k ≥ 3, we construct k-uniform linear hypergraphs G with arbitrarily large maximum degree Δ whose independence polynomial Z_G has a root λ with |λ| = O(\fraclog ΔΔ). This disproves a recent conjecture of Galvin, McKinley, Perkins, Sarantis, and Tetali.

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