On Conway's Thrackle Conjecture

A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many edges as vertices. Some related problems and generalizations are also considered.

• Type: Conference
• Year: 1995
• Where: COMPGEOM
• Authors: László Lovász, János Pach, Mario Szegedy
• Keywords: COMPGEOM 1995, Discrete Geometry, Distinct Arcs, Jordan Arcs, Thrackle