A note on the duality between matchings and vertex covers in balanced hypergraphs

We present a new Min-Max theorem for an optimization problem closely connected to matchings and vertex covers in balanced hypergraphs. The result generalizes Kőnig’s Theorem (Berge and Las Vergnas in Ann N Y Acad Sci 175:32–40, 1970 ; Fulkerson et al. in Math Progr Study 1:120–132, 1974 ) and Hall’s Theorem (Conforti et al. in Combinatorica 16:325–329, 1996 ) for balanced hypergraphs.