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Originally Posted by Pem
Feel free to prove me wrong - but I don't think you can do it with two straight lines even if you allow them to cross.
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You can't... You're esentially turning this into a bipartite graph. Using elementary combinatorics, it can be proven that this graph can't be turned into a bipartite graph because the total number of edges in conjunction with the 5 vertices requires a tripartite graph to exist.
You can even apply the 2-color, or 3-color theorem to this graph.