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  3. let g be a bipartite graph with 107 left vertices

Let G be a bipartite graph with 107 left vertices and 20 right vertices. Two vertices...

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Advance Math

  1. Let G be a bipartite graph with 107 left vertices and 20 rightvertices. Two vertices u, v are called twins if the set ofneighbors of u equals the set of neighbors of v (triplets,quadruplets etc are defined similarly).

    Show that G has twins.
    Bonus: Show that G has triplets. What about quadruplets, etc.?

Answer & Explanation Solved by verified expert
4.2 Ratings (541 Votes)
Suppose that there are elements on the leftand elements on the right Then the way we can make a graph such thatthere are no twins is by using the following algorithmSelect the first vertex on the left and do not join it to anyother vertex on the rightSelect next vertices on the leftand join it to the right vertices in a one onone manner Notice that we are not supposed to keep any vertexempty hence this followsNow note that you can form    See Answer
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