in hypergraphs

(a.k.a. minimal dominating sets in graphs)

Université Blaise Pascal, France

Room 1409

In this talk I will review some known results. In particular I will show that the Transversal problem is polynomially reduced to the enumeration of minimal dominating sets in co-bipartite graphs. A dominating set in a graph is a subset of vertices that intersect the closed neighborhood of every vertex. This interesting connection, we hope, will help in solving the Transversal problem by bringing structural graph theory into this area. I will also review new graph classes where we obtain polynomial delay algorithm for listing the minimal dominating sets. The talk will emphasize on the known techniques rather than a listing of known tractable cases.