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Total domination in K₅- and K₆-covered graphs

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.
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Odile Favaron, H. Karami, S. M. Sheikholeslami. Total domination in K₅- and K₆-covered graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, Vol. 10 no. 1 (1), pp.35--42. ⟨10.46298/dmtcs.433⟩. ⟨hal-00972309⟩



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