Splittable and unsplittable graphs and configurations - Bašić, Nino (Ars mathematica contemporanea, 2019)
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 Möbius-Kantor configuration are splittable.
Keywords: ciklični Haarov graf; configuration of points and lines; cyclic Haar graph; Grünbaum graph; Grünbaumov graf; independent set; konfiguracija točk in premic; Levi graph; Levijev graf; neodvisna množica vozlišč; nerazcepna konfiguracije; nerazcepni graf; razcepni tip; splitting type; unsplittable configuration; unsplittable graph