Suppose that $G$ is a 5-regular graph and 4-edge connected graph, I want to prove that every edge is in some perfect matching.
I can prove that for any edge $xy$, the graph $G-\{ xy\}$(delete the edge $xy$ from $G$) has a perfect matching by using Tutte's Theorem, however, I cannot derive the conclusion from what I have proved. Can anyone please help?