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Let g be a bipartite graph with bipartition sets vi v2 and

Question: Let g be a bipartite graph with bipartition sets VI, V2 and assume that g has a perfect matching. Add two vertices x and y to G such that x is adjacent to all vertices in V1, y is adjacent to all vertices in V2, and x is not adjacent to y.

(a) Show that G U {x, y} is bipartite.

(b) Show that GU {x, yl has a perfect matching.

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Mathematics: Let g be a bipartite graph with bipartition sets vi v2 and

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Mathematics: Let g be a bipartite graph with bipartition sets vi v2 and

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