Circuit mengerian directed graphs

Abstract

A feedback set of a digraph D = (V, E) is a set of vertices and edges such that its removal makes the digraph acyclic. Let w: V ∪ E — Z+ be a non-negative cost function. We say that D is Circuit Mengerian if, for every non-negative cost function w, the minimum weight feedback set is equal to the cardinality of the largest collection of circuits F with the property that, for every element t ∈ V∪E, no more than w(t) circuits of F use t. This property is closed under digraph minors, thus Circuit Mengerian digraphs can be characterized by a list of minor minimal non Circuit Mengerian digraphs. In this paper we give such an excluded minor characterization.