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

Let $\tau (G)$ 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 $$k+1\le s\le 2k-1,$$ together with a characterization of the associated extremal graphs. In this paper, we completely resolve this problem.