# Tutte's disjoint tree theorem

From Egres Open

**Theorem (Tutte)**^{[1]}. An undirected graph *G=(V,E)* contains *k* edge-disjoint spanning trees if and only if
if it is k-partition-connected.

This can be regarded as a special case of the Matroid union theorem. Sometimes it is referred to as the Tutte-Nash-Williams theorem because it also appears in the paper of Nash-Williams ^{[2]}.