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Annular and pants thrackles

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posted on 2023-05-24, 04:16 authored by Grace Omollo Misereh, Yury NikolayevskyYury 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 ≤ 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).

History

Publication Date

2018-05-25

Journal

Discrete Mathematics and Theoretical Computer Science

Volume

20

Issue

1

Article Number

16

Pagination

17p.

Publisher

Discrete Mathematics and Theoretical Computer Science (DMTCS)

ISSN

1365-8050

Rights Statement

© 2018 by the author(s) Distributed under a Creative Commons Attribution 4.0 International License

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