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arXiv · 2603.03966

Spectral radius and rainbow Hamiltonicity in bipartite graphs

Meng chen·Ruifang Liu·Qixuan Yuan
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Abstract

Let $\mathcal{G}=\{G_1, G_2, \ldots , G_k\}$ be a family of bipartite graphs on the same vertex set. A rainbow Hamilton path (cycle) in $\mathcal{G}$ is a path (cycle) that visits each vertex precisely once such that any two edges belong to different graphs of $\mathcal{G}.$ In this paper, by adopting the technique of bi-shifting, we present tight sufficient conditions in terms of the spectral radius for a family $\mathcal{G}$ to admit a rainbow Hamilton path and cycle, respectively. Meanwhile, we completely characterize the corresponding spectral extremal graphs.

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Meng chen, Ruifang Liu, Qixuan Yuan. 2026-03-04. Spectral radius and rainbow Hamiltonicity in bipartite graphs. https://arxiv.org/abs/2603.03966

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