Spectral radius and edge-disjoint spanning trees of graphs with edge connectivity
Jia Wei, Muhuo Liu, Zhifu You, Hong-Jian Lai
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 \[ k+1≤ s≤2k-1, \] together with a characterization of the associated extremal graphs. In this paper, we completely resolve this problem.
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