Cubic Graphs with Total Domatic Number at Least Two - Akbari Saieed (Discussiones Mathematicae Graph Theory, 2018)
Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two.