  Matchings and coverings are central topics in graph theory. The close
relationship between these two has been key to many fundamental algorithmic and
polyhedral results. For mixed graphs, the notion of matching forest was
proposed as a common generalization of matchings and branchings.
  In this paper, we propose the notion of mixed edge cover as a covering
counterpart of matching forest, and extend the matching--covering framework to
mixed graphs. While algorithmic and polyhedral results extend fairly easily,
partition problems are considerably more difficult in the mixed case. We
address the problems of partitioning a mixed graph into matching forests or
mixed edge covers, so that all parts are equal with respect to some criterion,
such as edge/arc numbers or total sizes. Moreover, we provide the best possible
multicriteria equalization.
