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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.

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    You’re welcome!2012-12-27

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