, Volume 35, Issue 3, pp 405-427

Small Triangle-Free Configurations of Points and Lines

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Abstract

In the paper we show that all combinatorial triangle-free configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (183) 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 (203) and the unique point transitive triangle-free configuration (213).