On the Independent Domination Number of Random Regular Graphs

A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either in v ∈ D or there exists a vertex u ∈ D that is adjacent to v. We are interested in finding dominating sets of small cardinality. A dominating set I of a graph G is said to be independent if no two vertices of I are connected by an edge of G. The size of a smallest independent dominating set of a graph G is the independent domination number of G. In this paper we present upper bounds on the independent domination number of random regular graphs. This is achieved by analysing the performance of a randomised greedy algorithm on random regular graphs using differential equations.