Let $\ell$ > r ≥ 3. Given a 2-graph F, the expansion F(r) of F is an r-graph obtained from F by adding r - 2 new vertices into each edge. When F is a clique of order $\ell$, the Turán number ex(n, F(r)) was first asymptotically determined by Mubayi (J Comb Theory Ser B 96:122-134, 2006) and exactly computed by Pikhurko (J Comb Theory Ser B 103:220-225, 2013). Let Fk,$\ell$ be the 2-graph on ($\ell$-1)k + 1 vertices consisting of k cliques of order $\ell$ intersecting at exactly one vertex. We determine the exact Turán number ex(n, Fk,$\ell$(3)) for all $\ell$ > 3, k ≥ 1 and sufficiently large n, as well as the corresponding extremal graphs.
Yu-Cong Tang, Tong Li, Gui-Ying Yan
. Turán Numbers of Expanded Intersecting Cliques in 3-graphs[J]. Journal of the Operations Research Society of China, 2024
, 12(4)
: 952
-964
.
DOI: 10.1007/s40305-022-00451-3
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