On the Bounds of Conway’s Thrackles

Luis Goddyn, Yian Xu

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)


    A thrackle on a surfaceX is a graph of size e and order n drawn on X such that every two distinct edges of G meet exactly once either at their common endpoint, or at a proper crossing. An unsolved conjecture of Conway (1969) asserts that (Formula presented.) for every thrackle on a sphere. Until now, the best known bound is (Formula presented.). By using discharging rules we show that (Formula presented.).

    Original languageEnglish
    Pages (from-to)410-416
    Number of pages7
    JournalDiscrete & Computational Geometry
    Issue number2
    Publication statusPublished - 1 Sep 2017


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