# Details of talk

Title Annulus and Pants Thrackle drawing Grace Omollo Misereh (La Trobe University) Grace Omollo Misere and Yuri Nikolayevsky Geometry and Topology 15:00:00 2017-09-25 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).