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

Joshua Erde, Pascal Gollin, Atilla Joó, Paul Knappe, Max Pitz

Published 2019-07-22Version 1

We show that if a graph admits a packing and a covering both consisting of $\lambda$ many spanning trees, where $\lambda$ is some infinite cardinal, then the graph also admits a decomposition into $\lambda$ many spanning trees. For finite $\lambda$ the analogous question remains open, however, a slightly weaker statement is proved.