An update on the middle levels problem

نویسندگان

  • Ian Shields
  • Brendan J. Shields
  • Carla D. Savage
چکیده

The middle levels problem is to find a Hamilton cycle in the middle levels, M2k+1, of the Hasse diagram of B2k+1 (the partially ordered set of subsets of a 2k + 1element set ordered by inclusion). Previously, the best known, from [1], was that M2k+1 is Hamiltonian for all positive k through k = 15. In this note we announce that M33 and M35 have Hamilton cycles. The result was achieved by an algorithmic improvement that made it possible to find a Hamilton path in a reduced graph (of complementary necklace pairs) having 129,644,790 vertices, using a 64-bit personal computer.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 309  شماره 

صفحات  -

تاریخ انتشار 2009