Grace Misereh ; Yuri Nikolayevsky - Annular and pants thrackles

dmtcs:3883 - Discrete Mathematics & Theoretical Computer Science, May 25, 2018, Vol. 20 no. 1 - https://doi.org/10.23638/DMTCS-20-1-16
Annular and pants thracklesArticle

Authors: Grace Misereh ; Yuri Nikolayevsky

    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).


    Volume: Vol. 20 no. 1
    Section: Graph Theory
    Published on: May 25, 2018
    Accepted on: April 27, 2018
    Submitted on: August 29, 2017
    Keywords: Mathematics - Combinatorics,Primary: 05C10, 05C62, Secondary: 68R10

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