Journal article

Conway's conjecture for monotone thrackles

A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conjecture for x-monotone thrackles, that is, in the case when every edge meets every vertical line in at most one point.


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