Splittable and unsplittable graphs and configurations
Nino Ba\v{s}i\'c, Jan Gro\v{s}elj, Branko Gr\"unbaum, Toma\v{z}, Pisanski
TL;DR
This paper investigates the properties of splittable and unsplittable cyclic configurations, providing infinite examples, analyzing small cases, and classifying flag-transitive configurations with respect to splittability.
Contribution
It establishes the existence of infinitely many splittable and unsplittable cyclic configurations and classifies most flag-transitive configurations based on splittability.
Findings
Existence of infinitely many splittable cyclic configurations.
Existence of infinitely many unsplittable cyclic configurations.
Most flag-transitive configurations are splittable, except Fano and M"obius-Kantor.
Abstract
We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic 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 M\"obius-Kantor configuration are splittable.
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