Interchangeability of Relevant Cycles in Graphs
AbstractThe 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.
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Bibliographic InfoPaper provided by Santa Fe Institute in its series Working Papers with number 99-07-046.
Date of creation: Jul 1999
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Minimum cycle basis; relevant cycles;
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