$\displaystyle G=(V,E)$ is a connected graph.
$\displaystyle H\subset E$. We suppose that for all $\displaystyle C$ cutset the number of $\displaystyle H\cap C$ is a even number.
Prove that $\displaystyle H$ is a cycle.
$\displaystyle G=(V,E)$ is a connected graph.
$\displaystyle H\subset E$. We suppose that for all $\displaystyle C$ cutset the number of $\displaystyle H\cap C$ is a even number.
Prove that $\displaystyle H$ is a cycle.
C is a cutset if there's a $\displaystyle X' \subset X$ so that
$\displaystyle C= w(X')$ = { $\displaystyle e=(i,j) \in E | i \in X' and\ j \not \in X'$},G - w(X') is connected and G - w isn't connected, $\displaystyle \forall w \subset w(X')$