### Abstract

A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one 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 problems and generalizations are also considered.

Original language | English |
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Pages (from-to) | 369-376 |

Number of pages | 8 |

Journal | Discrete and Computational Geometry |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1997 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Lovász, L., Pach, J., & Szegedy, M. (1997). On Conway's thrackle conjecture.

*Discrete and Computational Geometry*,*18*(4), 369-376. https://doi.org/10.1007/PL00009322