A thrackle is an embedding of a graph in the plane in which each edge is a Jordan arc and every pair of edges meet exactly once. Edges may either meet at a common endpoint, or, if they have no endpoints in common, at a point in their interiors. In the latter case, they must cross at their intersection point: the intersection must be transverse.[1]
^Lovász, L.; Pach, J.; Szegedy, M. (1997), "On Conway's thrackle conjecture", Discrete and Computational Geometry, 18 (4): 369–376, doi:10.1007/PL00009322, MR 1476318. A preliminary version of these results was reviewed in O'Rourke, J. (1995), "Computational geometry column 26", ACM SIGACT News, 26 (2): 15–17, arXiv:cs/9908007, doi:10.1145/202840.202842.
A thrackle is an embedding of a graph in the plane in which each edge is a Jordan arc and every pair of edges meet exactly once. Edges may either meet...
The Conway knot is named after him. Conway's conjecture that, in any thrackle, the number of edges is at most equal to the number of vertices, is still...
all antipodal pairs; the set of all pairs, viewed as a graph, forms a thrackle. The method of rotating calipers can be interpreted as the projective dual...
a thrackle (a graph drawn so that every pair of edges has one point of intersection) is also a thrackle, so Conway's conjecture that every thrackle has...
a complete graph with the same chromatic number Conway's thrackle conjecture that thrackles cannot have more edges than vertices The GNRS conjecture on...
game resembling peg solitaire Conway's thrackle conjecture – In graph theory, the conjecture that no thrackle has more edges than vertices Alexander–Conway...
Collatz 1440 Cramér's conjecture number theory Harald Cramér 32 Conway's thrackle conjecture graph theory John Horton Conway 150 Deligne conjecture monodromy...
common interior point at which the two edges properly cross. Conway's thrackle conjecture can now be reformulated as follows: A simple topological graph...
Conway's 99-graph problem, the minimum spacing of Danzer sets, and the thrackle conjecture. Guy, Richard K. (1976). "Twenty questions concerning Conway's...
including Conway's 99-graph problem, the analysis of sylver coinage, and the thrackle conjecture. Heilbronn triangle problem, on sets of points that do not form...
the n = 8 case, both involved a case analysis of all possible n-vertex thrackles with straight edges. The full conjecture of Graham, characterizing the...
that cross an odd number of times. The final chapter of part II concerns thrackles and the problem of finding drawings with a maximum number of crossings...
Global Information