On the total domination subdivision number in graphs

A set S ? V of vertices in a graph G = (V,E) without isolated vertices is a total dominating set if every vertex of V is adjacent to some vertex in S. The total domination number ?t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sd?t (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that sd?t (G) ? ? 0 (G) +1 for some classes of graphs where ? 0 (G) is the maximum cardinality of a matching of G.