Incidence structures near configurations of type (n_3)

Authors

DOI:

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

Keywords:

Geometric configurations, incidence structures

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.

Published

2020-10-26

Issue

Section

Articles