TITLE: Perfect matching in a 2-regular graph
QUESTION [0 upvotes]: Is it true, that in every $2$-regular graph with $14$ vertices there is a perfect matching ? If you think it's true - prove it, otherwise show counter-example
This is my exercise. I think that it's true because it doesn't matter how do you draw this graph, it always will be a cycle, and because the cycle has even number of vertices there always will be a perfect matching.

REPLY [2 votes]: HINT: Try making it a pair of $7$-cycles.
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