Computational Complexity of the Perfect Matching Problem in Hypergraphs with Subcritical Density

@article{Karpinski2010ComputationalCO,
  title={Computational Complexity of the Perfect Matching Problem in Hypergraphs with Subcritical Density},
  author={Marek Karpinski and Andrzej Rucinski and Edyta Szymańska},
  journal={Int. J. Found. Comput. Sci.},
  year={2010},
  volume={21},
  pages={905-924}
}
In this paper we consider the computational complexity of deciding the existence of a perfect matching in certain classes of dense k-uniform hypergraphs. It has been known that the perfect matching problem for the classes of hypergraphs H with minimum ((k l)-wise) vertex degree o(H) at least clV(H)1 is NP-complete for c< -!;; and trivial for c 2': ~, leaving the status of the problem with c in the interval [-!;;, ~) widely open. In this paper we show, somehow surprisingly, that ~ is not the… CONTINUE READING

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