Packing Non-Returning A-Paths*

Chudnovsky et al. gave a min-max formula for the maximum number of node-disjoint nonzero A-paths in group-labeled graphs [1], which is a generalization of Mader's theorem on node-disjoint A-paths [3]. Here we present a further generalization with a shorter proof. The main feature of Theorem 2.1 is that parity is “hidden” inside $\ifmmode\expandafter\hat\else\expandafter\^\fi{v}$, which is given by an oracle for non-bipartite matching.