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Math Help - Eular path and Eular Circut

  1. #1
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    Eular path and Eular Circut

    (a) Determine exactly when a complete graph Kn has an Euler path or Euler circuit.
    (b) Determine exactly when a complete bipartite graph Km,n has an Euler path or Euler circuit.
    (c) In the cases where Kn does not have an Euler path or Euler circuit, determine the smallest number of edges that need be removed for the graph to contain an Euler path or Euler circuit.

    I tried mant times to solve this but I couldn't.
    I know that an path is a path that travels through every edge of a graph once and only once; an Euler circuit is an Euler path thatstarts and ends at the same vertex.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Do you know/understand the conditions for an Euler circuit/path?

    A graph has an Euler circuit if and only if all vertices have even degree.

    A graph has an Euler path if and only if all vertices but precicely two have even degee.
    Last edited by Plato; May 22nd 2009 at 03:42 AM.
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