For $A\subseteq \{1,\dots ,n\}$ let $G(A)$ be the graph with vertex set $A$, where two integers are joined by an edge if they are coprime.Is it true that if$$|A|>\lfloor \frac{n}{2}\rfloor +\lfloor \frac{n}{3}\rfloor -\lfloor \frac{n}{6}\rfloor$$then $G(A)$ contains all odd cycles of length $\le \frac{n}{3}+1$?Is it true that, for every $\ell \ge 1$, if $n$ is sufficiently large and$$|A|>\lfloor \frac{n}{2}\rfloor +\lfloor \frac{n}{3}\rfloor -\lfloor \frac{n}{6}\rfloor$$then $G(A)$ must contain a complete $(1,\ell ,\ell )$ triparite graph on $2\ell +1$ vertices?