Geodesic
The maximal length of a gap between \(r\)-graph Turán densities
Oleg Pikhurko1
1University of Warwick
The electronic journal of combinatorics, Tome 22 (2015) no. 4
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The Turán density $\pi(\cal F)$ of a family $\cal F$ of $r$-graphs is the limit as $n\to\infty$ of the maximum edge density of an $\cal F$-free $r$-graph on $n$ vertices. Erdős [Israel J. Math, 2 (1964):183—190] proved that no Turán density can lie in the open interval $(0,r!/r^r)$. Here we show that any other open subinterval of $[0,1]$ avoiding Turán densities has strictly smaller length. In particular, this implies a conjecture of Grosu [arXiv:1403.4653, 2014].
DOI : 10.37236/5170
Classification : 05C42, 05C65, 05D05
Mots-clés : hypergraphs, Turán function

Oleg Pikhurko  1

1 University of Warwick 
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Oleg Pikhurko. The maximal length of a gap between \(r\)-graph Turán densities. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5170

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