A note on a conjecture of Bene Watts–Norin–Yepremyan for Lagrangian

Pingge Chen, Biao Wu and Qianju Zhang

Applied Mathematics and Computation, 2022, vol. 427, issue C

Abstract: What is the maximum Lagrangian of an r-uniform hypergraph that is t-intersecting? For t=1, the answer is complete; the case r=3 was determined by Hefetz and Keevash in 2012, and the remaining cases r≥4 were determined by Bene Watts, Norin and Yepremyan in 2018. For integers n,r,t,i with 1≤t≤r≤n and 0≤i≤r−t, letF(n,r,t,i):={e∈([n]r):|e∩[t+2i]|≥t+i}be a t-intersecting r-uniform hypergraph. Bene Watts, Norin and Yepremyan further conjectured that if an r-graph G is t-intersecting, thenλ(G)≤max0≤i≤r−tlimn→∞λ(F(n,r,t,i)).In this paper, we confirm the conjecture for t∈{r−1,r−2}, and r∈{3,4,5,6}.

Keywords: Hypergraph Lagrangian; t-intersecting; Extremal problem (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002296

DOI: 10.1016/j.amc.2022.127151

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