Let $f(n)$ be the
maximum number of edges in a graph on $n$ vertices in which no two
cycles have the same length. Erd\"{o}s raised the problem of
determining $f(n)$. Erd\"{o}s conjectured that there exists a
positive constant $c$ such that $ex(n,C_{2k})\geq cn^{1+1/k}$.
Haj\'{o}s conjecture that every simple even graph on $n$ vertices can
be decomposed into at most $n/2$ cycles. We present the problems,
conjectures related to these problems and we summarize the know results.
We do not think Haj\'{o}s conjecture is true.