On the Fractional Covering Number of Hypergraphs

The fractional covering numberτ^* of a hypergraph $H = ( V, E )$ is defined to be the minimum possible value of ∑x ∈ V t( x ) where t ranges over all functions t : V → R which satisfy ∑x ∈ e t ( x ) 1 for all edges e ∈ E. In the case of ordinary graphs G, it is known that 2τ^* ( G ) is always an integer. By contrast, it is shown (among other things) that for any rational p/q 1, there is a 3-uniform hypergraph H with τ^* ( H ) = p/q.