Simultaneous graph parameters: Factor domination and factor total domination

Let F1,F2,…,FkF1,F2,…,Fk be graphs with the same vertex set VV. A subset S⊆VS⊆V is a factor dominating set if in every FiFi every vertex not in S is adjacent to a vertex in S  , and a factor total dominating set if in every FiFi every vertex in VV is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. In this note, we investigate bounds on the factor (total) domination number. These bounds exploit results on colorings of graphs and transversals of hypergraphs.