### 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.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2019.7.1.11

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