Pairs of Disjoint Dominating Sets and the Minimum Degree of Graphs

摘要

For a connected graph G of order n and minimum degree δ we prove the existence of two disjoint dominating sets D ₁ and D ₂ such that, if δ ≥ 2, then unless G = C ₄, and, if δ ≥ 5, then . While for the first estimate there are exactly six extremal graphs which are all of order 7, the second estimate is asymptotically best-possible.