Further results on maximal nontraceable graphs of smallest size

Abstract : Let g(n) denote the minimum number of edges of a maximal nontraceable (MNT) graph of order n. In 2005 Frick and Singleton (Lower bound for the size of maximal nontraceable graphs, Electronic Journal of Combinatorics, 12(1) R32, 2005) proved that g(n) = ⌈3n-22 ⌉ for n ≥54 as well as for n ∈I, where I= 12,13,22,23,30,31,38,39, 40,41,42,43,46,47,48,49,50,51 and they determined g(n) for n ≤9. We determine g(n) for 18 of the remaining 26 values of n, showing that g(n) = ⌈ 3n-22 ⌉ for n ≥54 as well as for n ∈I ∪18,19,20,21,24,25,26,27,28, 29,32,33 and g(n) = ⌈ 3n2 ⌉ for n ∈ 10, 11, 14, 15, 16, 17. We give results based on ''analytic'' proofs as well as computer searches.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 1 (1), pp.75--92
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00990607
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : mardi 13 mai 2014 - 16:28:51
Dernière modification le : jeudi 7 septembre 2017 - 01:03:40
Document(s) archivé(s) le : lundi 10 avril 2017 - 22:33:31

Fichier

2136-7732-1-PB.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00990607, version 1

Collections

Citation

Alewyn Petrus Burger, Joy Elizabeth Singleton. Further results on maximal nontraceable graphs of smallest size. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 1 (1), pp.75--92. 〈hal-00990607〉

Partager

Métriques

Consultations de la notice

196

Téléchargements de fichiers

693