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  3. 2. let g be a bipartite graph with 10^7 left verti

2. Let G be a bipartite graph with 10^7 left vertices and 20 right vertices. Two...

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Advance Math

2. Let G be a bipartite graph with 10^7 left vertices and 20right vertices. 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. Showthat G has triplets. What about quadruplets, etc.?

3. Show that there exists a bipartite graph with 10^5 leftvertices and 20 right vertices without any twins.

4. Show that any graph with n vertices and ?(G) ? n/2 + 1 has atriangle.

Answer & Explanation Solved by verified expert
3.8 Ratings (352 Votes)
2 First partThe set of neighbours of a left vertex is a subset of the setof the right vertices Since there are of right verticesthere are subsets of right vertices Thus the set of neighbours of a leftvertex must be one of these subsets of right vertices Now suppose that there are    See Answer
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