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Small Triangle-Free Configurations of Points and Lines

Authors:	Marko Boben Branko Grunbaum Tomaz Pisanski Arjana Zitnik

Affiliation:	(1) Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;(2) Department of Mathematics, University of Washington, Seattle, WA 98195, USA

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).

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