On the total domatic number of regular graphs
Hamideh Aram, Seyed Mahmoud Sheikholeslami, Lutz Volkmann · DOAJ (DOAJ: Directory of Open Access Journals) · 2012
A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domatic number of a graph G is the maximum number of total dominating sets into which the vertex set of G can be partitioned. We show that the total domatic number of a random r-regular graph is almost surely at most r