Erdős-Rényi and random regular graphs asymptotically satisfy the Itai-Zehavi conjecture, containing (1-o(1))np and (1-o(1))d independent spanning trees, with a d/4-factor guarantee for sparse regular graphs.
Censor-Hillel, M
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Approximate Itai-Zehavi conjecture for random graphs
Erdős-Rényi and random regular graphs asymptotically satisfy the Itai-Zehavi conjecture, containing (1-o(1))np and (1-o(1))d independent spanning trees, with a d/4-factor guarantee for sparse regular graphs.