Factor domination and minimum degree Original Research Article

For a graph G=(V,E), a factor F of G is a subgraph of G on the same vertex set, V. A subset S⊆V is a dominating set of G if every vertex v∈V–S is adjacent, in G, to a vertex of S. Let F1,F2,…,Fk be factors of G. A set S⊆V that is, simultaneously, a dominating set of Fi for each i with 1⩽i⩽k is called a factor dominating set of F1,F2,…,Fk. The cardinality of a smallest such set is called the factor domination number of F1,F2,…,Fk and denoted by γ(F1,F2,…,Fk). In this paper, we give bounds on γ(F1,F2,…,Fk) in terms of the minimum degrees of the Fi.