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  3. problem 8. a bipartite graph g = (v,e) is a graph

Problem 8. A bipartite graph G = (V,E) is a graph whose vertices can be partitioned into...

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Advance Math

Problem 8. A bipartite graphG = (V,E) is a graph whose vertices canbe partitioned into two (disjoint) sets V1 andV2, such that every edge joins a vertex inV1 with a vertex in V2.This means no edges are within V1 orV2 (or symbolically: ?u, v? V1, {u,v}? E and ?u,v ?V2, {u,v} ? E).

8(a) Show that the complete graph K2 is abipartite graph.

8(b) Prove that no complete graphKn, where n > 2, is abipartite graph.

8(c) Prove that every rooted tree forms a bipartite graph.

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