Vertex Cover on 4-Regular Hyper-graphs Is Hard to Approximate within 2 - \epsilon

• Authors: Jonas Holmerin
• Venue: CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
• Year: 2002

We prove that Minimum vertex cover on 4-regular hyper-graphs (or in other words, hitting set where all sets have size exactly 4), is hard to approximate within 2 - epsilon. We also prove that the maximization version, in which we are allowed to pick B = pn elements in an n-vertex hyper-graph, and are asked to cover as many edges as possible,is hard to approximate within 1/(1 - (1-p)^4) - epsilon when p geq 1/2 and within ((1-p)^4 + p^4)/(1 - (1-p)^4) - epsilon when p