Notes on the 33-point Erd\H{o}s--Szekeres problem
Combinatorics
2026-01-01 v1 Computational Geometry
Abstract
The determination of is the first open case of the planar Erd\H{o}s--Szekeres problem, where the general conjecture predicts . We present a SAT encoding for the 33-point case based on triple-orientation variables and a 4-set convexity criterion for excluding convex 7-gons, together with convex-layer anchoring constraints. The framework yields UNSAT certificates for a collection of anchored subfamilies. We also report pronounced runtime variability across configurations, including heavy-tailed behavior that currently dominates the computational effort and motivates further encoding refinements.
Cite
@article{arxiv.2512.24061,
title = {Notes on the 33-point Erd\H{o}s--Szekeres problem},
author = {Bogdan Dumitru},
journal= {arXiv preprint arXiv:2512.24061},
year = {2026}
}