Is there any result about the time complexity of finding a cycle of fixed length $k$ in a general graph?
All I know is that [Alon, Yuster and Zwick](http://www.tau.ac.il/~nogaa/PDFS/col5.pdf) use a technique called "color-coding",
which has a running time of $O(M(n))$, where $n$ is the number of vertices of the input graph and $M(n)$ is the time required to multiply two $n \times n$
matrices.

Is there any better result?