A thrackle is an embedding of a graph in the plane in which every pair of edges meets exactly once, either at a shared endpoint or at a single transverse crossing point in their interiors. Conway's thrackle conjecture, proposed by John H. Conway, states more generally that every thrackle has at most as many edges as vertices. It remains open; it is known only that the number of edges in a thrackle is at most a constant multiple of the number of vertices. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementIn any thrackle, the number of edges is at most equal to the number of vertices. 1 Prize StatusA prize of 1000 dollars was offered by John H. Conway for proving or disproving the conjecture; unclaimed, since the conjecture remains open. 1 Progress Toward ResolutionOpen. The current record bound is 1.393n edges for a thrackle with n vertices. 1 Classification
Resolution Status Prize Status
Prize Status (category)Prize Offered, Unclaimed 1 Connections
Sources
1. Conway's Thrackle Conjecture (Wikipedia)
Wikimedia FoundationLead section
John H. Conway conjectured more generally that every thrackle has at most as many edges as vertices.
Thrackle conjecture section
John H. Conway conjectured that, in any thrackle, the number of edges is at most equal to the number of vertices.
Progress section, Fulek and Pach
the current record is 1.393n
Thrackle conjecture section, prize sentence
Conway offered a $1000 prize for proving or disproving this conjecture
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