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arXiv · 1708.07351

Annular and pants thrackles

Grace Misereh·Yuri Nikolayevsky
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Abstract

A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of a graph on the plane cannot have more edges than vertices. We prove the Conjecture for thrackle drawings all of whose vertices lie on the boundaries of $d \le 3$ connected domains in the complement of the drawing. We also give a detailed description of thrackle drawings corresponding to the cases when $d=2$ (annular thrackles) and $d=3$ (pants thrackles).

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Grace Misereh, Yuri Nikolayevsky. 2018-05-22. Annular and pants thrackles. https://doi.org/10.23638/dmtcs-20-1-16

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