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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

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Minimum modifications to make a graph bipartite

Let's say I have a graph that is not bipartite. Let's say it is colored red and black and there are some conflicts where two vertices of the same color share an edge. I can introduce a new vertex betw …