The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex cover number (i.e., size of a minimum vertex cover) for a bipartite graph. More generally, the theorem states that the maximum size of a partial matching in a relation equals the minimum size of a separating set.

bipartite graph | Frobenius-König theorem | König's line coloring theorem | König's theorem | matching number | maximum independent edge set | minimum vertex cover | separating family | vertex cover number