Asymptotic behavior for joint Turán number for \(3\) and \(4\)cycles
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For a finite family \( {\mathcal F}\) of graphs, let \( t(n, {\mathcal{F}})\) denote the smallest integer \( m\) that every graph on \( n\) vertices and \( m\) edges must contain a member of \( \mathcal{F}\) as a subgraph. Erdös and Simonovits [1] raised the following question:
A problem on the Turán number of \(C_3\) and \(C_4\)[1]
Is it true that \[ t(n,\{C_3,C_4\}) = \frac 1 {2 \sqrt 2} n^{3/2} + O(n)~ ?\]
Bibliography  

1 
P. Erdös and M. Simonovits, Compactness results in extremal graph
theory, Combinatorica 2 (1982), 275288.
