Packings and 2-packings of A-paths

We investigate the relation between packings and 2-packings of A-paths. We show a similarity to the relation between matchings and 2-matchings in graphs. The former needs parity arguments, while the latter admits a Kőnig-type characterization. The algorithmic method of proof also yields – as a by-product – a generalization of the odd ear-decomposition of a factor-critical graph. For packing non-returning A-paths there are two different natural notions of criticality, we show a decomposition for both. An odd ear-decomposition can be given for (strongly) criticals. For weakly criticals a so-called dragon-decomposition can be given – a decomposition in a specific way into a forest and some strongly criticals.