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I must find out for what values of n and m the complete bipartite graph K(n,m) is eulerian.Can you give me some sugestions or hints to where to start ?I know the definitions but I don't know where to begin to solve this problem.

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Hint: A connected graph is Eulerian if and only if every vertex has what property?

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every vertex has even degree –  user910 Feb 1 '13 at 13:21
    
@EmilGrigore Not the same degree--rather, if and only if every vertex has even degree. –  Andrew Uzzell Feb 1 '13 at 13:24
    
so the number of edges must be even –  user910 Feb 1 '13 at 13:27
    
@EmilGrigore Yes, that's true--but is that enough? –  Andrew Uzzell Feb 1 '13 at 13:37
    
well every vertex from K has the same number of edges as the number of vertexes in the opposed set of vertexes.So for example:if one set contains 1,2 and another set contains 3,4,5,6,the vertexes 1,2 will have each 4 edges and the vertexes 3,4,5,6 will each have 2 vertexes.For it to be an eulerian graph,also the sets of vertexes needs to contain an even number of vertexes. –  user910 Feb 1 '13 at 13:49
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