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We know that every 2-colourable graph is bipartite. To prove that we divide the vertices having different colors and put them separately in 2 partitions.

Suppose there are n vertices in an empty graph and they are randomly colored as 1 and 2. The ones with '1' are placed in partition A and those with '2' are placed in partition B . Can this be called a bipartite case even when there is no connection b/w the vertices of partition A and B? If not, why?
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