Construction of 2-factors in the middle layer of the discrete cube

Details Construction of 2-factors in the middle layer of the discrete cube Construction of 2-factors in the middle layer of the discrete cube

2011-11-10

arxiv.org/abs/1111.2413v1

Mathematics

Combinatorics

Scientific paper

Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length $2n+1$ that have exactly $n$ or $n+1$ entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. In this work we present an inductive construction of a large family of 2-factors in the middle layer graph for all $n\geq 1$. We also investigate how the choice of certain parameters used in the construction affects the number and lengths of the cycles in the resulting 2-factor.

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