Minimum independent generalized t-degree and independence number in K1,r+1-free graphs Original Research Article

The minimum independent generalized t-degree of a graph G = (V, E) is ut = min{|N(H)|; H is an independent set of t vertices of G}, with N(H) = ∪x∈H N(x). In a K1,r+1-free graph, we give an upper bound on ut in terms of r and the independence number α of G. This generalizes already known results on u2 in K1,r+1-free graphs and on ut in K1,3-free graphs.