A thrackle is a graph drawn in the plane so that its vertices are represented by points and its edges are represented by continuous arcs so that any pair of edges meet precisely once: either at a common endpoint or at a proper crossing. Almost half a century ago Conway conjectured that every thrackle has at most as many edges as vertices. Why is this question interesting? Where do we stand now? We also report on some recent results joint with Radoslav Fulek (EPFL).
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