Maximum-cardinality matching in general graphs in almost-linear time

Theorem 1.1: a single uniform randomized algorithm finds a maximum-cardinality matching of any simple graph in $(n+m)^{1+o(1)}$ word operations on every path, with success probability at least $2/3$ and explicit output. Corollary: the same guarantees for deciding and constructing $f$-factors (prescribed-degree spanning subgraphs). It is randomized (no deterministic version), unweighted (maximum-weight general matching is not addressed), and the $o(1)$ is not made explicit.

Theorem 1.1: a single uniform randomized algorithm finds a maximum-cardinality matching of any simple graph in $(n+m)^{1+o(1)}$ word operations on every path, with success probability at least $2/3$ and explicit output. Corollary: the same guarantees for deciding and constructing $f$-factors (prescribed-degree spanning subgraphs). It is randomized (no deterministic version), unweighted (maximum-weight general matching is not addressed), and the $o(1)$ is not made explicit.