Elsevier

Discrete Mathematics

Volume 321, 28 April 2014, Pages 35-44
Discrete Mathematics

Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges

https://doi.org/10.1016/j.disc.2013.12.014Get rights and content
Under an Elsevier user license
open archive

Abstract

Ruskey and Savage asked the following question: for n2, does every matching in Qn extend to a Hamiltonian cycle in Qn? Fink showed that the answer is yes for every perfect matching, thereby proving Kreweras’ conjecture. In this paper we consider the question in hypercubes with faulty edges. We show for n2 that every matching M of at most 2n1 edges extends to a Hamiltonian cycle in Qn. Moreover, we prove that when n4 and M is nonempty this conclusion still holds even if Qn has at most n1|M|2 faulty edges, with one exception.

Keywords

Hypercube
Hamiltonian cycle
Matching
Edge fault-tolerance

Cited by (0)

This work is supported by NSFC (grant nos. 61073046, 11371180).