A New Upper Bound for Conway’s Thrackles

Yian Xu

Applied Mathematics and Computation, 2021, vol. 389, issue C

Abstract: If G=(V,E) has a drawing on the plane where two different edges have a proper crossing if and only if they are non-adjacent, then we call such a drawing a thrackle. Conway conjectured |E| is no more than |V| for thrackles. This paper shows that |E| is no more than 1.393(|V|−1).

Keywords: Thrackles; Discharging rule; Planar; 2-cell embedding; Euler’s formula (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305294

DOI: 10.1016/j.amc.2020.125573

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