Discrete & Computational Geometry

, Volume 35, Issue 3, pp 405–427 | Cite as

Small Triangle-Free Configurations of Points and Lines

  • Marko Boben
  • Branko Grunbaum
  • Tomaz Pisanski
  • Arjana Zitnik


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).


Computational Mathematic Unique Point Geometric Realization Petersen Graph Generalize Petersen Graph 
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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, University of Ljubljana, 1000 LjubljanaSlovenia
  2. 2.Department of Mathematics, University of Washington, Seattle, WA 98195USA

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