On a conjecture concerning total domination subdivision number in graphs. Issue 3 (2nd September 2021) - Kosari, S.; Shao, Z.; Khoeilar, R.; Karami, H.; Sheikholeslami, S. M.; Hao, G.
Abstract: Let γ t ( G ) be the total domination number and let sd γ t ( G ) be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that sd γ t ( G ) ≤ γ t ( G ) / 2 + 2 for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.