DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 23(2) (2003) 241-260
DOI: 10.7151/dmgt.1200

CIRCUIT BASES OF STRONGLY CONNECTED DIGRAPHS

Petra M. Gleiss

Institute for Theoretical Chemistry and Structural Biology
University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria
e-mail: pmg@tbi.univie.ac.at

Josef Leydold

Department for Applied Statistics and Data Processing
University of Economics and Business Administration
Augasse 2-6, A-1090 Wien, Austria
e-mail: Josef.Leydold@statistik.wu-wien.ac.at

Peter F. Stadler

Institute for Theoretical Chemistry and Structural Biology
University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria

The Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe NM 87501, USA
and
Bioinformatics Group, Department of Computer Science
University of Leipzig, Kreuzstrasse 7b, D-04103 Leipzig, Germany
e-mail: studla@bioinf.uni-leipzig.de

Abstract

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.

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

2000 Mathematics Subject Classification: 05C20 (directed graphs), 05C38 (paths and cycles), 05C85 (graph algorithms).

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Received 28 September 2001
Revised 16 May 2002