Intersecting spanning trees for general graphs

Determine the independence number of the spanning tree disjointness graph for graph classes beyond complete graphs, thereby characterizing maximum families of pairwise edge-intersecting spanning trees in more general graphs.

Background

The paper studies the independence number of the spanning tree disjointness graph for the complete graph K_n. Independent sets in this graph correspond to families of spanning trees whose members share at least one edge pairwise. The authors explicitly restrict their main work to K_n and identify analogous questions for more general graph classes as unresolved.