Are all 2-colorable graphs bipartite?

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I believe bipartite means you can split the vertices of a graph into 2 groups, where each vertex in the first is connected to all in the second (correct me if Im wrong) Does that mean every 2-colorable graph is bipartite? If not, what are some counterexamples, and an explanation why?

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Yes, in fact bipartite is equivalent to 2-colorable.