Kőnig's edge-colouring theorem for all graphs

We show that the maximum degree of a graph G is equal to theminimum number of ocm sets covering G, where an ocm set is the vertex-disjoint union of elementary odd cycles and onematching, and a collection of ocm sets covers G if every edge is in the matching of an ocm set or in some odd cycle of at least two ocm sets. © 2013 Elsevier B.V. All rights reserved.