Partitioning Bispanning Graphs into Spanning Trees

Abstract

Given a weighted bispanning graph B = (V, P, Q) consisting of two edge-disjoint spanning trees P and Q such that w(P ) < w(Q) and Q is the only spanning tree with weight w(Q), it is conjectured that there are |V | − 1 spanning trees with pairwise different weight where each of them is smaller than w(Q). This conjecture due to Mayr and Plaxton is proven for bispanning graphs restricted in terms of the underlying weight function and the structure of the bispanning graphs. Furthermore, a slightly stronger conjecture is presented and proven for the latter class.