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Crossings Between Non-homotopic Edges

János Pach, Gábor Tardos, Géza Tóth
2020-06-26

We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on \(n>1\) vertices can have arbitrarily many edges.

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