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In: Advanced Math

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

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

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

8(b) Prove that no complete graph Kn, where n > 2, is a bipartite graph.

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

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