The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles in W and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class W. This result is used to derive upper and lower bounds on the number of distinct minimum cycle bases. Finally, we give a polynomial-time algorithm to compute this partition. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing
| Identifer | oai:union.ndltd.org:VIENNA/oai:epub.wu-wien.ac.at:epub-wu-01_9e1 |
| Date | January 1999 |
| Creators | Gleiss, Petra M., Leydold, Josef, Stadler, Peter F. |
| Publisher | Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business |
| Source Sets | Wirtschaftsuniversität Wien |
| Language | English |
| Detected Language | English |
| Type | Paper, NonPeerReviewed |
| Format | application/pdf |
| Relation | http://epub.wu.ac.at/898/ |
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