In this paper we present an algorithmic approach to packing A-paths. It is regarded as a generalization of Edmonds' matching algorithm, however there is the significant difference that here we do not build up any kind of alternating tree. Instead we use the so-called 3-way lemma, which either provides augmentation, or a dual, or a subgraph which can be used for contraction. The method works in the general setting of packing non-returning A-paths. It also implies an ear-decomposition of criticals, as a generalization of the odd ear-decomposition of factor-critical graph.
Hiroshi Hirai;Gyula Pap, 2013, Tree metrics and edge-disjoint $$S$$ S -paths, Mathematical Programming, 147, 1-2, pp. 81-123, 10.1007/s10107-013-0713-5.
Maxim A. Babenko, 2008, A Fast Algorithm for the Path 2-Packing Problem, Theory of computing systems (Print), 46, 1, pp. 59-79, 10.1007/s00224-008-9141-y.
Maxim A. Babenko, Lecture notes in computer science, A Fast Algorithm for Path 2-Packing Problem, pp. 70-81, 2007, 10.1007/978-3-540-74510-5_10.