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

Abstract

The minimum independent generalized t-degree of a graph G = ( V, E) is u t = min{| N( H)|; H is an independent set of t vertices of G}, with N( H) = ∪ x∈ H N( x). In a K 1, r+1 -free graph, we give an upper bound on u t in terms of r and the independence number α of G. This generalizes already known results on u 2 in K 1, r+1 -free graphs and on u t in K 1,3-free graphs.