English

Matchings of quadratic size extend to long cycles in hypercubes

Discrete Mathematics 2023-06-22 v3

Abstract

Ruskey and Savage in 1993 asked whether every matching in a hypercube can be extended to a Hamiltonian cycle. A positive answer is known for perfect matchings, but the general case has been resolved only for matchings of linear size. In this paper we show that there is a quadratic function q(n)q(n) such that every matching in the nn-dimensional hypercube of size at most q(n)q(n) may be extended to a cycle which covers at least 34\frac34 of the vertices.

Keywords

Cite

@article{arxiv.1511.06568,
  title  = {Matchings of quadratic size extend to long cycles in hypercubes},
  author = {Tomáš Dvořák},
  journal= {arXiv preprint arXiv:1511.06568},
  year   = {2023}
}