Covering Intersecting Bi-set Families under Matroid Constraints

Edmonds’ fundamental theorem on arborescences [4] characterizes the existence of k pairwise edge-disjoint arborescences with the same root in a directed graph. In [9], Lovász gave an elegant alternative proof which became the base of many extensions of Edmonds’ result. In this paper, we use a modification of Lovász’ method to prove a theorem on covering intersecting bi-set families under matroid constraints. Our result can be considered as a common generalization of previous results on packing arborescences.