Journal of Combinatorial Optimization

, Volume 32, Issue 2, pp 639–644 | Cite as

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.


Matching Vertex cover Hypergraph Balanced hypergraph Duality Koenig’s Theorem Hall’s Theorem 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Lehrstuhl II für MathematikRWTH AachenAachenGermany

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