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Article Dans Une Revue Computational Geometry Année : 2014

Enumerating topological $(n_k)$-configurations

Résumé

An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. We provide an algorithm for generating, for given $n$ and $k$, all topological $(n_k)$-configurations up to combinatorial isomorphism, without enumerating first all combinatorial $(n_k)$-configurations. We apply this algorithm to confirm efficiently a former result on topological $(18_4)$-configurations, from which we obtain a new geometric $(18_4)$-configuration. Preliminary results on $(19_4)$-configurations are also briefly reported.
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Dates et versions

hal-01276787 , version 1 (23-02-2016)

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Jürgen Bokowski, Vincent Pilaud. Enumerating topological $(n_k)$-configurations. Computational Geometry, 2014, Special Issue: 23rd Canadian Conference on Computational Geometry (CCCG11), 47 (2, Part A), pp.175-186. ⟨10.1016/j.comgeo.2012.10.002⟩. ⟨hal-01276787⟩
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