A short proof of the middle levels theorem

10/23/2017

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by   Petr Gregor, et al.

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Consider the graph that has as vertices all bitstrings of length 2n+1 with exactly n or n+1 entries equal to 1, and an edge between any two bitstrings that differ in exactly one bit. The well-known middle levels conjecture asserts that this graph has a Hamilton cycle for any n≥ 1. In this paper we present a new proof of this conjecture, which is much shorter and more accessible than the original proof.