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Many Turan exponents via subdivisions | | Tao Jiang
; Yu Qiu
; | | Date: |
7 Aug 2019 | | Abstract: | Given a graph $H$ and a positive integer $n$, the {it Tur’an number}
$ex(n,H)$ is the maximum number of edges in an $n$-vertex graph that does not
contain $H$ as a subgraph. A real number $rin(1,2)$ is called a {it Tur’an
exponent} if there exists a bipartite graph $H$ such that
$ex(n,H)=Theta(n^r)$. A long-standing conjecture of ErdH{o}s and Simonovits
states that $1+frac{p}{q}$ is a Tur’an exponent for all positive integers $p$
and $q$ with $q> p$.
In this paper, we build on recent developments on the conjecture to establish
a large family of new Tur’an exponents. In particular, it follows from our
main result that $1+frac{p}{q}$ is a Tur’an exponent for all positive
integers $p$ and $q$ with $q> p^2$. | | Source: | arXiv, 1908.2385 | | Services: | Forum | Review | PDF | Favorites | |
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