2017/08/16 by Péter G. N. Szabó, Szabó, Péter G. N. · 1 citation
Engineering · #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1708.05075
openalex publication_date 2017/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One way to study the combinatorics of finite metric spaces is to study the betweenness relation associated with the metric space. In the hypergraph metrization problem, one has to find and characterize metric betweennesses whose collinear triples (or alternatively, non-degenerate triangles) coincide with the edges of a given 3-uniform hypergraph. Metrizability of different kinds of hypergraphs was investigated in the last decades. Chen showed that steiner triple systems are not metrizable, while Richmond and Richmond characterized linear betweennesses, i.e. metric betweennesses that realize the complete 3-uniform hypergraph. The latter result was also generalized to almost-metric betweennesses by Beaudou et al. In this paper, we further extend this theory by characterizing the largest nonlinear almost-metric betweennesses that satisfy certain hereditary properties, as well as the ones that contain a small linear number of non-degenerate triangles.