Circuit bases of strongly connected digraphs. (English) Zbl 1055.05068

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

Discuss. Math., Graph Theory 23, No. 2, 241-260 (2003).

Summary: 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.

MSC:

05C20	Directed graphs (digraphs), tournaments
05C38	Paths and cycles
05C85	Graph algorithms (graph-theoretic aspects)

Keywords:

directed graphs; cycle space; relevant circuits; minimum length basis