Splittable and unsplittable graphs and configurations

Nino Bašić, Jan Grošelj, Branko Grünbaum, Tomaž Pisanski


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.


Configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph

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DOI: https://doi.org/10.26493/1855-3974.1467.04b

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications