Abstract
A strengthened version of a previous conjecture of the author is considered. The former version of the conjecture was that if every subset of a given setA of vertices in a hypergraph is connected to a set of edges with ‘large’ matching number, thenA is matchable. Here we suggest that it is possible to assume only large fractional matching numbers. We prove the conjecture in the case ∣A∣ = 2, and also a fractional version of the conjecture.
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References
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Kessler, O.: Matchings in hypergraphs. D.Sc. thesis, Technion, 1989.
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Aharoni, R. On a criterion for matchability in hypergraphs. Graphs and Combinatorics 9, 209–212 (1993). https://doi.org/10.1007/BF02988309
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DOI: https://doi.org/10.1007/BF02988309