On the fractional matching polytope of a hypergraph


For a hypergraph ℋ andb:ℋ→ℝ+ define

Conjecture. There is a matching ℳ of ℋ such that

For uniform ℋ andb constant this is the main theorem of [4]. Here we prove the conjecture if ℋ is uniform or intersecting, orb is constant.

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Additional information

The research was done while the author visited the Department of Mathematics at Rutgers University. Research supported in part by the Hungarian National Science Foundation under grant No. 1812

Supported in party by NSF and AFOSR grants and by a Sloan Research Fellowship

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Füredi, Z., Kahn, J. & Seymour, P.D. On the fractional matching polytope of a hypergraph. Combinatorica 13, 167–180 (1993). https://doi.org/10.1007/BF01303202

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AMS Subject Classification Code (1991)

  • 05 D 15