Write an algorithm that deterimines if an arbitrary, Basic Computer Science

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Write an algorithm that deterimines if an arbitrary

1. Prove that a tree is a bipartite graph.

2. Prove that any tree can be two-colored.

3. Write an algorithm that deterimines if an arbitrary undirected graph is a bipartite graph. If the graph is bipartite, then your algorithm should also identify the vertices as to which of the two partitions each belongs to.

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