2006/10/01 by G Szekeres, Lindsay Peters · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Computational Geometry and Mesh Generation #Conjecture #Signature (topology) #Planar #Simple (philosophy) #Regular polygon #Point (geometry) #Set (abstract data type) #Computer science #Combinatorics #Proof of concept #Mathematics #Algorithm #Discrete mathematics #Geometry #Computer graphics (images) #Programming language
paper · pdf · doi:10.1017/s144618110000300x
openalex publication_date 2006/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the “Happy End Problem”) that a planar configuration of 17 points, no 3 points collinear, always contains a convex 6-subset. The proof makes use of a combinatorial model of planar configurations, expressed in terms of signature functions satisfying certain simple necessary conditions. The proof is more general than the original conjecture as the signature functions examined represent a larger set of configurations than those which are realisable. Three independent implementations of the computer proof have been developed, establishing that the result is readily reproducible.