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arXiv · 2610.18574

Spectral radius and edge-disjoint spanning trees of graphs with edge connectivity

Jia Wei·Muhuo Liu·Zhifu You·Hong-Jian Lai
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Abstract

Let $τ(G)$ denote the maximum number of pairwise edge-disjoint spanning trees contained in a graph $G$. Zhang and Fan [J. Graph Theory, 2026] posed the problem of determining the corresponding tight spectral-radius condition for every $s$-edge-connected graph with \[ k+1\leq s\leq2k-1, \] together with a characterization of the associated extremal graphs. In this paper, we completely resolve this problem.

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Jia Wei, Muhuo Liu, Zhifu You, Hong-Jian Lai. 2026-10-13. Spectral radius and edge-disjoint spanning trees of graphs with edge connectivity. https://arxiv.org/abs/2610.18574

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