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Interchangeability of Relevant Cycles in Graphs

Author

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  • Petra M. Gleiss
  • Josef Leydold
  • Peter F. Stadler

Abstract

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 and 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.

Suggested Citation

  • Petra M. Gleiss & Josef Leydold & Peter F. Stadler, 1999. "Interchangeability of Relevant Cycles in Graphs," Working Papers 99-07-046, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:99-07-046
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    1. Petra M. Gleiss & Peter F. Stadler, 1999. "Relevant Cycles in Biopolymers and Random Graphs," Working Papers 99-07-042, Santa Fe Institute.
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      Keywords

      Minimum cycle basis; relevant cycles;

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