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⊆ 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 α _k(H) . In this paper, we give a lower bound of α _k(H) for H in terms of its maximum degree. Furthermore, we prove for all k≥ 0 that α _k(H)≥s(k+1)n/2d+s(k+1) , where d is the average degree of H .