Generalised independent minimum t-degree - Domke G.S.; Markus L.R. (Utilitas Mathematica, 2002)
Let G be a connected graph on n vertices. Let β0(G) denote the cardinality of a largest independent set of vertices in G. For 1 ≤ t ≤ β0(G), the generalised independent minimum t-degree, δti(G), is defined as follows: δti(G) = min|N(S)|: S is an independent set with t vertices. We show that for any graph G, β0(G)+δti(G) ≤ n for all t, 1 ≤ t ≤ β0(G). Furthermore, we present necessary and sufficient conditions for certain classes of graphs to achieve β0(G) + δti(G) = n.