## Misereh, Grace and Nikolayevsky, Yuri - Annular and pants thrackles

dmtcs:3883 - Discrete Mathematics & Theoretical Computer Science, May 25, 2018, Vol. 20 no. 1
Annular and pants thrackles

Authors: Misereh, Grace and Nikolayevsky, Yuri

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).

Source : oai:arXiv.org:1708.07351
DOI : 10.23638/DMTCS-20-1-16
Volume: Vol. 20 no. 1
Section: Graph Theory
Published on: May 25, 2018
Submitted on: August 29, 2017
Keywords: Mathematics - Combinatorics,Primary: 05C10, 05C62, Secondary: 68R10