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It's known that every cubic bridgeless graph has 1-factor (Petersen). 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 - theorem 2.1.)

Thanks in advance

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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

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  • $\begingroup$ unfortunately, it's a german article :( but thanks $\endgroup$
    – Rafael Korbas
    Commented Nov 2, 2013 at 19:09
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    $\begingroup$ ok I found an english source proving this: link $\endgroup$
    – Rafael Korbas
    Commented Nov 2, 2013 at 22:52

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