### Total domination in K_{5}- and K_{6}-covered graphs

*Odile Favaron, Hosein Karami, Seyed Mahmoud Sheikholeslami*

#### Abstract

A graph G is K

_{r}-covered if each vertex of G is contained in a K_{r}-clique. Let γ_{t}(G) denote the total domination number of G. It has been conjectured that every K_{r}-covered graph of order n with no K_{r}-component satisfies γ_{t}(G) ≤ 2n/(r+1). We prove that this conjecture is true for r=5 and 6.Full Text: PDF PostScript