Transversal partitioning in balanced hypergraphs

Abstract

A transversal of a hypergraph is a set of vertices meeting all the hyperedges. A k-fold transversal Ω of a hypergraph is a set of vertices such that every hyperedge has at least k elements of Ω. In this paper, we prove that a k-fold transversal of a balanced hypergraph can be expressed as a union of k pairwise disjoint transversals and such partition can be obtained in polynomial time. We give an NC algorithm to partition a k-fold transversal of a totally balanced hypergraph into k pairwise disjoint transversals. As a corollary, we deduce that the domatic partition problem is in polynomial class for chordal graphs with no induced odd trampoline and is in NC-class for strongly chordal graphs.