• Corpus ID: 239024756

Great-circle Tree Thrackles

  title={Great-circle Tree Thrackles},
  author={Karen L. Collins and Cleo Roberts},
A thrackle is a graph drawing in which every pair of edges meets exactly once. Conway’s Thrackle Conjecture states that the number of edges of a thrackle cannot exceed the number of its vertices. Cairns et al (2015) prove that the Thrackle Conjecture holds for great-circle thrackles drawn on the sphere. They also posit that Conway’s Thrackle Conjecture can be restated to say that a graph can be drawn as a thrackle drawing in the plane if and only if it admits a great-circle thrackle drawing. We… 


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  • Computer Science, Mathematics
    Appl. Math. Comput.
  • 2021
This paper shows that |E| is no more than 1.393 ( | V | − 1 ) for thrackles.
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We establish Conway's thrackle conjecture in the case of great-circle thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.
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Combinatorial Mathematics and its Applications
  • Chap. Thrackles and deadlock
  • 1971