I need some help to see if the definition I found of Cycles and Cycles Decomposition is right, here it is:
A graph is a Cycle if it is isomorph to another graph $G=(V,E)$ with the following proprieties: $V=\{v_0,v_1,\ldots,v_m\}$ and $(v_i,v_j)\in E$ if and only if $|i-j|=1$ or $|i-j|=m$.
A graph is Decomposible in Cycles if it is an Edge-disjoint union of Cycles
This bring me to see the graph $C_2=(V,E)$, $V=\{v_0,v_1\}$, $E=\{(v_0,v_1)\}$ (the simple "dot-line-dot" graph) as Cycle, but if it is then every graph can be decomposed in a series of $C_2$ Cycles.
(I aplogize both for the english, definition are actually translated form french, and for the bad formatting)
If someone know a better definition or see where the error is in my conclusion it would be helpfull.
Thanks, Midkar.