Geodesic
Incidence structures near configurations of type (n_3)
Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 17-23.

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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.
DOI : 10.26493/1855-3974.1685.395
Keywords: Geometric configurations, incidence structures 
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Peter J. Dukes; Kaoruko Iwasaki. Incidence structures near configurations of type (n_3). Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 17-23. doi : 10.26493/1855-3974.1685.395. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1685.395/

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