2 problems

Let $z(n)$ denote the maximum number of edges in a bipartite graph with partite sets of order $n$ that contains no cycle of length four. For a prime power $k$, consider the order…

Let $C_k$ denote a cycle of length $k$. Let $\operatorname{ex}(n,\{C_3,C_4\})$ be the maximum number of edges in a graph on $n$ vertices containing no triangle or four-cycle, and l…