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Math Help - Cycles

  1. #1
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    Cycles

    A cycle is defined to be a circuit with no repeasted vertex. If a cycle has length k, we talk of a k-cycle. Determine the number of 4-cycles in Km,n where m > 2 and n > 2.

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  2. #2
    Junior Member guildmage's Avatar
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    I'm not a graph theorist, but I think since we are considering K_{m,n} for m,n \geq 2, then any four distinct vertices -- 2 coming from the set of m vertices and 2 coming from the set of n vertices -- will make a 4-cycle. So that there will be \left( \begin{array}{l} m \\ 2 \\ \end{array} \right) \left( \begin{array}{l} n \\ 2 \\ \end{array} \right) ways of choosing such a collection of 4 vertices.
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