Theory of linear and integer programming
Theory of linear and integer programming
Characterization of even directed graphs
Journal of Combinatorial Theory Series B
A Min-Max Theorem on Feedback Vertex Sets
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
A TDI System and Its Application to Approximation Algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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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.