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 such that every matching in the -dimensional hypercube of size at most may be extended to a cycle which covers at least 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}
}