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A computational approach to Conway's thrackle conjecture
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 number of edges that a thrackle of n vertices can have.
According to a 40 years old conjecture of Conway, t(n)=n for every n>2. For any
eps>0, we give an algorithm terminating in e^{O((1/eps^2)ln(1/eps))} steps to
decide whether t(n)2. Using this approach, we improve the
best known upper bound, t(n)<=3/2(n-1), due to Cairns and Nikolayevsky, to
167/117n<1.428n.Comment: 16 pages, 7 figure