S. Akbari, M. Motiei, S. Mozaffari, S. Yazdanbod
Cubic graphs with total domatic number at least two
Discussiones Mathematicae Graph Theory
Received 26.02.2016, Revised 28.09.2016, Accepted 28.09.2016, doi: 10.7151/dmgt.1996
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.
total domination, total domatic number, coupon coloring