Spanning tree with equal number of red and blue edges

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1. The balanced spanning tree problem is the following problem: given a graph G with edges that are eitherred or blue, determine if there is a spanning tree with an equal number of red and blue edges. For anarbitrary graph G, give an efficient algorithm for determining if G has a balanced spanning tree. (It doesn'thave to be as efficient as possible, but be reasonable!)

2. Suppose G is a graph such that G - e is a tree for every edge e ∈ EG. Prove that G is isomorphic to a cycle. (Be careful: it is not sufficient to show that if G is a cycle, then G - e is a tree for every e ∈ EG)

Reference no: EM132396222

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