{"docId":433,"paperId":433,"url":"https:\/\/dmtcs.episciences.org\/433","doi":"10.46298\/dmtcs.433","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":83,"name":"Vol. 10 no. 1"}],"section":[{"sid":16,"title":"Graph and Algorithms","description":[]}],"repositoryName":"Hal","repositoryIdentifier":"hal-00972309","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00972309v1","dateSubmitted":"2015-03-26 16:20:03","dateAccepted":"2015-06-09 14:46:55","datePublished":"2008-01-01 08:00:00","titles":{"en":"Total domination in K\u2085- and K\u2086-covered graphs"},"authors":["Favaron, Odile","Karami, H.","Sheikholeslami, S. M."],"abstracts":{"0":"Graphs and Algorithms","en":"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 satis\ufb01es $\\gamma_t(G) \\le \\frac{2n}{r+1}$. We prove that this conjecture is true for r = 5 and 6."},"keywords":["[INFO.INFO-DM] Computer Science [cs]\/Discrete Mathematics [cs.DM]"]}