Year: 2026
Type: preprint
Abstract: Bondy and Tuza generalized the Turán problem for graphs to weighted graphs. Subsequently, Füredi and Kündgen gave a solution in the case of cliques. We consider the weighted Turán problem on hypergraphs and prove the first tight asymptotic result for 3-uniform hypergraphs. Specifically, we determine the weighted Turán density of the generalized triangle $F_5 = \{abc, abd, cde\}$. We also prove weighted stability results and exact results. Many intriguing open problems remain, the most tantalizing of which is to determine the weighted Turán density of the tetrahedron. Bounds for this density using flag algebras are presented.
Source: arXiv (Cornell University)
Authors: James, David, Lidický, Bernard, Mubayi, Dhruv
Institutions: University of Illinois Chicago, Iowa State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7224872192