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    Post Reopened by Fedor Petrov, Gil Kalai, Sergei Ivanov, Tony Huynh, Joseph O'Rourke

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Draw the complete graph $K_n$ in the plane [added: in general position] with every edge a straight line and randomly label the edges $0$ or $1$. Does this graph always have a spanning tree with no edges crossing and edge-labels either all $0$ or all $1$?

    Post Closed as "too localized" by S. Carnahan

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