Work

Separating hypergraph Turán densities

Year: 2025

Type: article

Abstract: Determining the Turán densities of hypergraphs is a notoriously difficult problem at the core of combinatorics. Although Turán posed this problem in 1941, the value of remains unknown for all . Prior to this work, it was not even known whether holds for general and , and the best‐known bounds on are far from implying anything close to this. We prove that , for all , and provide general criteria to distinguish the Turán densities of two hypergraphs. As a corollary, we also obtain that , for all . For , this was previously proved by Markström, answering a question by Erdős.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70195

Authors: Hong Liu, Bjarne Schülke, Shuaichao Wang, Haotian Yang, Yixiao Zhang

Institutions: Institute for Basic Science, Nankai University, California Institute of Technology, Fuzhou University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Shandong University, China Scholarship Council, Institute for Basic Science, National Key Research and Development Program of China

Awards: G2765210714, G2809982917