Long cycles in hypercubes with distant faulty vertices - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2009

Long cycles in hypercubes with distant faulty vertices

Abstract

In this paper, we study long cycles in induced subgraphs of hypercubes obtained by removing a given set of faulty vertices such that every two faults are distant. First, we show that every induced subgraph of Q(n) with minimum degree n - 1 contains a cycle of length at least 2(n) - 2(f) where f is the number of removed vertices. This length is the best possible when all removed vertices are from the same bipartite class of Q(n). Next, we prove that every induced subgraph of Q(n) obtained by removing vertices of some given set M of edges of Q(n) contains a Hamiltonian cycle if every two edges of M are at distance at least 3. The last result shows that the shell of every linear code with odd minimum distance at least 3 contains a Hamiltonian cycle. In all these results we obtain significantly more tolerable faulty vertices than in the previously known results. We also conjecture that every induced subgraph of Q(n) obtained by removing a balanced set of vertices with minimum distance at least 3 contains a Hamiltonian cycle.
Fichier principal
Vignette du fichier
1005-4198-3-PB.pdf (192.81 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00988176 , version 1 (07-05-2014)

Identifiers

Cite

Petr Gregor, Riste Škrekovski. Long cycles in hypercubes with distant faulty vertices. Discrete Mathematics and Theoretical Computer Science, 2009, Vol. 11 no. 1 (1), pp.185--198. ⟨10.46298/dmtcs.466⟩. ⟨hal-00988176⟩

Collections

TDS-MACS
81 View
873 Download

Altmetric

Share

Gmail Facebook X LinkedIn More