# Math Help - Cutsets in graph theory.

1. ## Cutsets and Cycles

$G=(V,E)$ is a connected graph.
$H\subset E$. We suppose that for all $C$ cutset the number of $H\cap C$ is a even number.

Prove that $H$ is a cycle.

2. C is a cutset if there's a $X' \subset X$ so that
$C= w(X')$ = { $e=(i,j) \in E | i \in X' and\ j \not \in X'$},G - w(X') is connected and G - w isn't connected, $\forall w \subset w(X')$