It's known that every cubic bridgeless graph has 1-factor ([Petersen](http://en.wikipedia.org/wiki/Petersen%27s_theorem)). But Does anybody know, how to prove that for every edge in a cubic bridgeless graph there exists a 1-factor, which contains it? 


Because I found articles, where this is stated, but no proof of it so far (for example this [one](http://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1731.pdf) - theorem 2.1.)


Thanks in advance



Union of perfect matchings in bridgeless cubic graphs
Petersen's theorem: A bridgeless cubic graph contains a one-factor.
This has been generalized by T. Schönberger [T. Schönberger, "Ein Beweis des Peterschen Graphensatzes" Acta Sci. Math. Szeged , 7 (1934) pp. 51–57], who proved that every edge of a bridgeless cubic graph lies in a one-factor.


Best regards,
 Július Korbaš 


