Work

Triangle-Free Triple Systems

Year: 2026

Type: article

Abstract: There are four non-isomorphic configurations of triples that can form a triangle in a $3$-uniform hypergraph. Forbidding different combinations of these four configurations, fifteen extremal problems can be defined, several of which already appeared in the literature. Here we systematically study all of these problems solving the new cases exactly or asymptotically. In many cases we also characterize the extremal constructions.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/14115

Authors: Peter Frankl, Zoltán Füredi, Ido Goorevitch, Ron Holzman, Gábor Simonyi

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Technion – Israel Institute of Technology, Budapest University of Technology and Economics

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, National Research, Development and Innovation Office