Circuit Bases of Strongly Connected Digraphs

Petra M. Gleiss, Josef Leydold, and Peter F. Stadler


The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.

Mathematics Subject Classification: 05C20 (directed graphs), 05C38 (paths and cycles), 05C85 (graph algorithms)

Keywords: graph theory, directed graphs, cycle space, relevant circuits, minimum length basis

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