Small Triangle-Free Configurations of Points and Lines

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).

Authors and Affiliations

1. Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

   Marko Boben, Tomaz Pisanski & Arjana Zitnik

2. Department of Mathematics, University of Washington, Seattle, WA 98195, USA

   Branko Grunbaum

Corresponding authors

Correspondence to Marko Boben, Branko Grunbaum, Tomaz Pisanski or Arjana Zitnik.

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