Kőnig’s edge-colouring theorem for all graphs
Résumé
We show that the maximum degree of a graph GG is equal to the minimum number of ocm sets covering GG, where an ocm set is the vertex-disjoint union of elementary odd cycles and one matching, and a collection of ocm sets covers GG if every edge is in the matching of an ocm set or in some odd cycle of at least two ocm sets.