Discrete & Computational Geometry

, Volume 35, Issue 3, pp 405–427

Small Triangle-Free Configurations of Points and Lines

Article

DOI: 10.1007/s00454-005-1224-9

Cite this article as:
Boben, M., Grunbaum, B., Pisanski, T. et al. Discrete Comput Geom (2006) 35: 405. doi:10.1007/s00454-005-1224-9

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).

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