\fbox{\parbox{5in}{{\it A decomposition problem of a complete graph} (propose... ...\par Determine $f(n)$. \par Is $f(n)$\ unbounded as $n \rightarrow \infty$? }}

Although this is a fairly old problem, relatively little is known. It can be easily shown that $ C_5$ and $ C_7$ can be avoided provided $ n$ is large.

Bibliography

1
P. Erd{\H{o\/}}\kern.05ems and R. L. Graham, On partition theorems for finite graphs, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erd{\H{o\/}}\kern.05ems on his 60th birthday), Vol. I; Colloq. Math. Soc. János Bolyai, Vol. 10, 515-527, North-Holland, Amsterdam, 1975.