Random Structures and Algorithms· 2026Q1
Random Turán Problems for Hypergraph Expansions
- 0citations
- Q1SCImago
- 2026year
Short summary
Researchers systematically studied the largest k-free subgraph of random hypergraph expansions, finding it exhibits three predictable phases for Sidorenko hypergraphs when k is large.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces the concept of k-free subgraphs within random hypergraph expansions.
- Identifies three predictable phases for these subgraphs in Sidorenko hypergraphs when k is large.
- Demonstrates more complex behavior when a hypergraph lacks a Sidorenko expansion.
- Unifies and generalizes existing results for random Turán problems in degenerate hypergraphs (uniformity >= 3).
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT Given an ‐uniform hypergraph , we define its ‐uniform expansion to be the hypergraph obtained from by inserting distinct vertices into each edge of , and we define to be the largest ‐free subgraph of the random hypergraph . We initiate the first systematic study of for general hypergraphs . Our main result essentially resolves this problem for large by showing that goes through three predictable phases whenever is Sidorenko and is sufficiently large, with the behavior of being provably more complex whenever has no Sidorenko expansion. Moreover, our methods unify and generalize almost all previously known results for the random Turán problem for degenerate hypergraphs of uniformity at least 3.
The authors' abstract, as published at the source. Random Structures and Algorithms, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics