Abstract : A graph G is Kr-covered if each vertex of G is contained in a Kr-clique. Let $\gamma_t(G)$ denote the total domination number of G. It has been conjectured that every Kr-covered graph of order n with no Kr-component satisfies $\gamma_t(G) \le \frac{2n}{r+1}$. We prove that this conjecture is true for r = 5 and 6.
https://hal.inria.fr/hal-00972309
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s
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Soumis le : jeudi 3 avril 2014 - 16:07:48
Dernière modification le : mardi 24 avril 2018 - 13:55:38
Document(s) archivé(s) le : jeudi 3 juillet 2014 - 16:31:00
Odile Favaron, H. Karami, S. M. Sheikholeslami. Total domination in K₅- and K₆-covered graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, 10 (1), pp.35--42. 〈hal-00972309〉
