Approximating the Domatic Number

A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a graph into the maximum number of disjoint dominating sets. Let n denote the number of vertices, the minimum degree, and the maximum degree. We show that every graph has a domatic partition with (1 - o(1))( + 1)/ ln n dominating sets and, moreover, that such a domatic partition can be found in polynomial-time. This implies a (1 + o(1)) ln n-approximation algorithm for domatic number, since the domatic number is always at most

• Type: Journal
• Year: 2002
• Where: SIAMCOMP
• Authors: Uriel Feige, Magnús M. Halldórsson, Guy Kortsarz, Aravind Srinivasan
• Keywords: Disjoint Dominating Sets, Domatic Number Problem, Maximum Number, SIAMCOMP 2002