Odile Favaron ; H. Karami ; S. M. Sheikholeslami - Total domination in K₅- and K₆-covered graphs

dmtcs:433 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, Vol. 10 no. 1 - https://doi.org/10.46298/dmtcs.433
Total domination in K₅- and K₆-covered graphs

Authors: Odile Favaron ; H. Karami ; S. M. Sheikholeslami

    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.


    Volume: Vol. 10 no. 1
    Section: Graph and Algorithms
    Published on: January 1, 2008
    Imported on: March 26, 2015
    Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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