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

Given an undirected graph G(V,E) and a vertex subset U\subseteq V the U-space is the vector space over GF(2) spanned by the paths with end-points in U and the cycles in G(V,E). We extend Vismara's algorithm to the computation of the union of all minimum length bases of the U-space. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing