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Math Help - graph theory question about walks and cycles

  1. #1
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    graph theory question about walks and cycles

    If a graph G has a closed walk of length at least three containing a vertex x, then G has a cycle
    containing x.

    Can anyone explain why this statement is true or false?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by lachicacomica View Post
    If a graph G has a closed walk of length at least three containing a vertex x, then G has a cycle
    containing x.

    Can anyone explain why this statement is true or false?
    Look at the definition of a closed walk and cycle. How do they compare?
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