Saturation problems in convex geometric hypergraphs. (May 2023)

• Record Type: Journal Article
• Authors: O'Neill, Jason; Spiro, Sam
• Is Part Of: European journal of combinatorics. Volume 110(2023)
• Publication Date: 2023-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2023.103702
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: A convex geometric hypergraph (abbreviated cgh) consists of a collection of subsets of a strictly convex set of points in the plane. Extremal problems for cgh's have been extensively studied in the literature, and in this paper we consider their corresponding saturation problems. We asymptotically determine the saturation number of two geometrically disjoint r -tuples. Further, amongst the eight nonisomorphic 3-uniform cgh's on two edges, we determine the saturation number for seven of these up to order of magnitude and the eighth up to a log factor.