A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely
once, either at a common vertex or at a proper crossing. Let t (n) denote the maximum …

We investigate under what conditions crossings of adjacent edges and pairs of edges
crossing an even number of times are unnecessary when drawing graphs. This leads us to …

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 …

In this paper we investigate how certain results related to the Hanani–Tutte theorem can be
extended from the plane to surfaces. We give a simple topological proof that the weak …

We show that a graph drawing is an outerplanar thrackle if and only if, up to an inversion in
the plane, it is Reidemeister equivalent to an odd musquash. This establishes Conway's …

A thrackle on a surface X is a graph of size e and order n drawn on X such that every two
distinct edges of G meet exactly once either at their common endpoint, or at a proper …

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once:
either at a common end vertex or in a proper crossing. We prove that any thrackle of n …

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Let P be a set of n points in general and convex position in the plane. Let D n be the graph
whose vertex set is the set of all line segments with endpoints in P, where disjoint segments …

We define the notion of a geometric graph in R^ 3. This is a graph drawn in R^ 3 with its
vertices drawn as points and its edges as straight line segments connecting corresponding …