Bounds on the domination number of Kneser graphs

Abstract

The Kneser graph KG n , k has one vertex for each k -subset of an n -set and edges between vertices whenever the corresponding subsets are disjoint. A dominating set in a graph G = ( V , E ) is a subset S ⊆ V such that each vertex in V \ S is adjacent to at least one vertex in S . The domination number of , denoted by γ ( n , k ) , is the minimum size of a dominating set in that graph. Combinatorial and computer-aided techniques for obtaining bounds on γ ( n , k ) are here considered, and several new bounds are obtained. An updated table of bounds on γ ( n , k ) is presented for n ≤ 21 and k ≤ 5 .