Greedoids from flames

Abstract

A digraph D with r ∈ V (D) is an r-flame if for every v ∈ V (D) − r, the in-degree of v is equal to the local edge-connectivity λ D (r, v). We show that for every digraph D and r ∈ V (D), the edge sets of the r-flame subgraphs of D form a greedoid. Our method yields a new proof of Lovász' theorem stating: for every digraph D and r ∈ V (D), there is an r-flame subdigraphWe also give a strongly polynomial algorithm to find such an F working with a fractional generalization of Lovász' theorem.