Small triangle-free configurations of points and lines

Abstract

In this paper we show that all combinatorial triangle-free configurations (v_3) for v (is less than or equal to) 8 are geometrically realizable. We also show that there is a unique smallest astral (18_3) triangle-free configuration, and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric realizations of the unique flag transitive triangle-free configuration (20_3) and the unique point transitive triangle-free configuration (21_3).