ON CONWAY THRACKLE CONJECTURE

Authors
LOVASZ L PACH J SZEGEDY M
Citation
L. Lovasz et al., ON CONWAY THRACKLE CONJECTURE, Discrete & computational geometry, 18(4), 1997, pp. 369-376
Citations number
21
Categorie Soggetti
Computer Sciences, Special Topics","Mathematics, General","Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
18
Issue
4
Year of publication
1997
Pages
369 - 376
Database
ISI
SICI code
0179-5376(1997)18:4<369:OCTC>2.0.ZU;2-E
Abstract
A thrackle is a graph drawn in the plane so that its edges are represe nted by Jordan arcs and any two distinct arcs either meet at exactly o ne common vertex or cross at exactly one point interior to both arcs. About 40 years ago, J. H. Conway conjectured that the number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many edges as vertices. Some related pr oblems and generalizations are also considered.