|Title||Annulus and Pants Thrackle drawing|
|Presenter||Grace Omollo Misereh (La Trobe University)|
|Author(s)||Grace Omollo Misere and Yuri Nikolayevsky|
|Session||Geometry and Topology|
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 $d\leq 3$ 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 $d = 3$ (pair of pants thrackles).
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