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- W1518155507 abstract "In this note, we show that for any $m in {1,2, dots , q +1 }$, if $G$ is a polarity graph of a projective plane of order $q$ that has an oval, then $G$ contains a subgraph on $m + binom{m}{2}$ vertices with $m^2+frac{m^4}{8q} - O ( frac{m^4}{q^{3/2} } +m )$ edges. As an application, we give the best known lower bounds on the Tur'{a}n number $mathrm{ex}(n, C_4)$ for certain values of $n$. In particular, we disprove a conjecture of Abreu, Balbuena, and Labbate concerning $mathrm{ex}(q^2-q-2, C_4)$ where $q$ is a power of $2$." @default.
- W1518155507 created "2016-06-24" @default.
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- W1518155507 date "2015-02-09" @default.
- W1518155507 modified "2023-09-23" @default.
- W1518155507 title "Small dense subgraphs of polarity graphs and the extremal number for the 4-cycle" @default.
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