Incidence structures near configurations of type (n3)

Peter J. Dukes, Kaoruko Iwasaki

Abstract


An (n3) configuration is an incidence structure equivalent to a linear hypergraph on n vertices which is both 3-regular and 3-uniform. We investigate a variant in which one constraint, say 3-regularity, is present, and we allow exactly one line to have size four, exactly one line to have size two, and all other lines to have size three. In particular, we study planar (Euclidean or projective) representations, settling the existence question and adapting Steinitz’ theorem for this setting.


Keywords


Configuration, incidence structure

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DOI: https://doi.org/10.26493/1855-3974.1685.395

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