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4. (6 points) A (simple undirected) graph is given by a collection of nodes, some pairs of which may be connected by edges. For which

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4. (6 points) A (simple undirected) graph is given by a collection of nodes, some pairs of which may be connected by edges. For which of the following graphs is it possible to color each node red or blue in such a way that no two adjacent nodes (nodes connected by an edge) are assigned the same color. Prove your answers

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