My question was to prove using Tutte theorem that $3$-regular graphs and $2$-edge-connected graphs have perfect matching.
For the $3$-regular-matching, i found the solution by myself, using Tutte's thorem $q(G-S)$ $\leq$ $|$S$|$, for any $S$ in $V$. ( I took a odd component, and made the sum of vertex)
But for the $2$-edge-connected graphs i can't find the connection between the Tutte relation?
Any hints/ideas for the $2$-edge-connected part?