Maximum cycle packing using SPR-trees

Abstract

Let G = ( V , E ) be an undirected multigraph without loops. The maximum cycle packing problem is to find a collection Z * = { C 1 , ..., C s } of edge-disjoint cycles C i subset G of maximum cardinality v ( G ) . In general, this problem is NP-hard. An approximation algorithm for computing v ( G ) for 2-connected graphs is presented, which is based on splits of G . It essentially uses the representation of the 3-connected components of G by its SPR-tree. It is proved that for generalized series-parallel multigraphs the algorithm is optimal, i.e. it determines a maximum cycle packing Z * in linear time.