A lower bound on the independence number of arbitrary hypergraphs

We present a lower bound on the independence number of arbitrary hypergraphs in terms of the degree vectors. The degree vector of a vertex v is given by d(v) = (d 1 (v); d 2 (v); : : :) where d m (v) is the number of edges of size m containing v. We deene a function f with the property that any hypergraph H = (V; E) satisses (H) P v2V f(d(v)). This lower bound is sharp when H is a matching, and it generalizes known bounds of Caro/Wei and Caro/Tuza for ordinary graphs and uniform hypergraphs. Furthermore, an algorithm for computing independent sets of size as guaranteed by the lower bound is given. c