Tolérance aux pannes dans les graphes distants et circulants

SETIT2005
présence d’un sommet/arête en panne. Ils sont 1
panne-tolérant hamiltonien.
Pour les graphes circulants Cn(1, r), nous avons
prouvé qu’un cycle hamiltonien est plongeable en
présence de deux arêtes en pannes si n ≥ 2r+1. Nous
avons prouvé aussi que l’on peut plonger un cycle
hamiltonien en présence de deux sommets en panne si
n ≥ 6r-6 et, dans certains cas, si 2r+2≤n2r+2 .
Les résultas obtenus dans notre travail représentent
le début de l’étude de la conjecture de Sung et al.
(Sung & al., 2000) , qui dit qu’un graphe circulant
C(n ;1,2,…,k) est k panne-tolérant hamiltonien.
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