(b): Theorem 2.4, page 34.Proofs were also done in class. These varied somewhat from thoseof the text._________________________________________________________________9. (10 pts.)(a) Suppose G is a bipartite graph of order atleast 5. Prove that the complement of G is not bipartite. [Hint:At least one partite set has three elements. Connect the dots?]Suppose that G is a bipartite graph of order at least 5 withpartite sets U and W. At least one of U and W has at least 3elements. Suppose without loss of generality, W≥3. Labelthree of the members of W with u,v, and w. Since these verticesare in the same partite set of G, none of these three vertices isadjacent to any other of the three. Thus,uv,vw,uw∈E(G)⇒G contains a3cycle.Thus, the complement of G is not bipartite. [Problem 1.25?](b) Display a bipartite graph G of order 4 and its bipartitecomplement. Label each appropriately and give partite sets foreach bipartite graph.//There are a multitude of examples. See me if you need helpwith this! This reveals why we want V(G)≥5 in (a).
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