Splittable and unsplittable graphs and configurations.

We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic (n(3)) 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 Mobius-Kantor configuration are splittable.