LAUSR

Let G be a graph. The Steiner distance of W ⊆ V (G) is the minimum size of a connected subgraph of G containing W . Such a subgraph is necessarily a tree called a Steiner W -tree. The set A ⊆ V (G) is a k-Steiner general position set if V (TB)∩A = B holds for every set B ⊆ A of cardinality k, and for every Steiner B-tree TB . The kSteiner general position number sgpk(G) of G is the cardinality of a largest k-Steiner general position set in G. This number is bounded from below by the cardinality of a largest k-Steiner clique. The k-Steiner general position number is determined for trees, cycles, joins of graphs and a lower bound is presented for lexicographic products, split graphs and infinite grids.