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arXiv · 2508.03778

A spectral condition for Hamilton cycles in tough bipartite graphs

Lianyang Ai·Wenqian Zhang
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Abstract

Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph $G$ with parts $X$ and $Y$, the {\em bipartite toughness} of $G$ is defined as $t^{B}(G)=\min\left\{\frac{|S|}{c(G-S)}\right\}$, where the minimum is taken over all proper subsets $S\subset X$ (or $S\subset Y$) such that $c(G-S)>1$. In this paper, we give a sharp spectral radius condition for balanced bipartite graphs $G$ with $t^{B}(G)\geq1$ to guarantee that $G$ contains Hamilton cycles. This solves a problem proposed in \cite{CFL}.

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Lianyang Ai, Wenqian Zhang. 2025-08-05. A spectral condition for Hamilton cycles in tough bipartite graphs. https://arxiv.org/abs/2508.03778

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