Union of perfect matchings in bridgeless cubic graphs - MathOverflow

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?

Union of perfect matchings in bridgeless cubic graphs - MathOverflow Union of perfect matchings in bridgeless cubic graphs Ask Question Asked 12 years, 8 months ago Modified 12 years, 8 months ago Viewed 350 times 0 $\begingroup$ 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 graph-theory Share Cite Improve this que

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