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 elementt ∈ 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.
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Guenin, B. (2001). Circuit Mengerian Directed Graphs. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_15
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DOI: https://doi.org/10.1007/3-540-45535-3_15
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