Splittable and unsplittable graphs and configurations
Keywords:Configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph
We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic (n3) configurations. We also present a complete study of trivalent cyclic Haar graphs on at most 60 vertices with respect to splittability. Finally, we show that all cyclic flag-transitive configurations with the exception of the Fano plane and the Möbius-Kantor configuration are splittable.