English

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

Combinatorics 2018-02-16 v1

Abstract

Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length 2n+12n+1 that have exactly nn or n+1n+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 n1n\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.

Keywords

Cite

@article{arxiv.1111.2413,
  title  = {Construction of 2-factors in the middle layer of the discrete cube},
  author = {Torsten Mütze and Franziska Weber},
  journal= {arXiv preprint arXiv:1111.2413},
  year   = {2018}
}