Enumerating tuples of spanning trees

Abstract

Deciding whether a graph has k-edge-disjoint spanning trees is a well-studied problem. We consider the problem of enumerating all sets of spanning trees with polynomial delay. This work is based on the alternate proof of Tutte and Nash-Williams' characterization of graphs with k edge-disjoint spanning trees by Kaiser [1]. The idea is to maintain a decision tree for all forest-packs and perform a Depth-First Search over it. We build this decision tree inductively by computing each node's children using a variant of Kaiser's technique [1].