186 research outputs found
The maximal length of a gap between r-graph Tur\'an densities
The Tur\'an density of a family of -graphs is the
limit as of the maximum edge density of an -free -graph
on vertices. Erdos [Israel J. Math 2 (1964) 183--190] proved that no
Tur\'an density can lie in the open interval . Here we show that
any other open subinterval of avoiding Tur\'an densities has strictly
smaller length. In particular, this implies a conjecture of Grosu [E-print
arXiv:1403.4653v1, 2014].Comment: 7 page
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