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Enumerating Perfect Matchings in n-Cubes

Abstract

The perfect matchings in the n-cube have earlier been enumerated for n ≤ 6. A dynamic programming approach is here used to obtain the total number of perfect matchings in the 7-cube, which is 391 689 748 492 473 664 721 077 609 089. The number of equivalence classes of perfect matchings is further shown to be 336 in the 5-cube, 356 788 059 in the 6-cube and 607 158 046 495 120 886 820 621 in the 7-cube. The techniques used can be generalized to arbitrary bipartite and general graphs.

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Correspondence to Ville H. Pettersson.

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Östergård, P.R.J., Pettersson, V.H. Enumerating Perfect Matchings in n-Cubes. Order 30, 821–835 (2013). https://doi.org/10.1007/s11083-012-9279-8

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Keywords

  • Perfect matching
  • N-cube
  • Dynamic programming
  • Enumeration