New Results on k-independence of Hypergraphs

Let H = (V, E) be an s-uniform hypergraph of order n and k >= 0 be an integer. A k-independent set S subset of V is a set of vertices such that the maximum degree in the hypergraph induced by S is at most k. The maximum cardinality of a k-independent set of H is denoted by alpha(k)(H). In this paper, we give a lower bound of alpha(k) (H) for H in terms of its maximum degree. Furthermore, we prove for all k >= 0 that alpha(k) (H) >= s(k+1)n/2d+s(k+1) , where d is the average degree of H.