An update on the middle levels problem
Combinatorics
2007-05-23 v1
Abstract
The middle levels problem is to find a Hamilton cycle in the middle levels, M_{2k+1}, of the Hasse diagram of B_{2k+1} (the partially ordered set of subsets of a 2k+1-element set ordered by inclusion). Previously, the best result was that M_{2k+1} is Hamiltonian for all positive k through k=15. In this note we announce that M_{33} and M_{35} 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.
Keywords
Cite
@article{arxiv.math/0608485,
title = {An update on the middle levels problem},
author = {Ian Shields and Brendan J. Shields and Carla D. Savage},
journal= {arXiv preprint arXiv:math/0608485},
year = {2007}
}
Comments
11 pages, 5 figures