Fractional matchings and covers in infinite hypergraphs

Abstract

A strong version of the duality theorem of linear programming is proved for fractional covers and matchings in countable graphs. It is conjectured to hold for general hypergraphs. In Section 2 we show that in countable hypergraphs there does not necessarily exist a maximal matchable set, contrary to the situation in graphs.

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Aharoni, R. Fractional matchings and covers in infinite hypergraphs. Combinatorica 5, 181–184 (1985). https://doi.org/10.1007/BF02579360

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AMS subject classification (1980)

  • 03 E 05
  • 04 A 05
  • 04 A 20