A Cantor-Bernstein-type theorem for spanning trees in infinite graphs

Abstract

We show that if a graph admits a packing and a covering both consisting of ? many spanning trees, where ? is some infinite cardinal, then the graph also admits a decomposition into ? many spanning trees. For finite ? the analogous question remains open, however, a slightly weaker statement is proved. ? 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).