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1 results

The codegree Turán density of tight cycles minus one edge
Part of
- Graph theory
- Extremal combinatorics
Simón Piga, Marcelo Sales, Bjarne Schülke
Journal:

Combinatorics, Probability and Computing / Volume 32 / Issue 6 / November 2023

Published online by Cambridge University Press:

05 July 2023, pp. 881-884
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Given $\alpha \gt 0$ and an integer $\ell \geq 5$, we prove that every sufficiently large $3$-uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $\alpha n$ edges contains a copy of $C_\ell ^{-}$, a tight cycle on $\ell$ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.