Covering a hypergraph of subgraphs

Let G be a tree and let H be a collection of subgraphs of G, each having at most d connected components. Let (H) denote the maximum number of members of H no two of which share a common vertex, and let (H) denote the minimum cardinality of a set of vertices of G that intersects all members of H. It is shown that (H) 2d2 (H). A similar, more general result is proved replacing the assumption that G is a tree by the assumption that it has a bounded tree-width. These improve and extend results of various researchers.

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Noga Alon
• Keywords: Common Vertex, DM 2002, Maximum Number, Tree