An upper bound of 61 for the Ramsey number $R(3,3,3,3)$

We improve the upper bound on the classical Ramsey number $R(3,3,3,3)$ from 62 to 61. The proof is based on a global incidence count, classifications of small neighborhoods and exhaustive SAT computations. We formalize the mathematical reductions in Lean and refute every resulting formula with two SAT solvers.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36648
Primary Topic
Limits and Structures in Graph Theory
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

An upper bound of 61 for the Ramsey number $R(3,3,3,3)$

Milos Tatarevic
arXiv (Cornell University)
Limits and Structures in Graph Theory
preprint

An upper bound of 61 for the Ramsey number $R(3,3,3,3)$

Milos Tatarevic
preprint en

Abstract

We improve the upper bound on the classical Ramsey number $R(3,3,3,3)$ from 62 to 61. The proof is based on a global incidence count, classifications of small neighborhoods and exhaustive SAT computations. We formalize the mathematical reductions in Lean and refute every resulting formula with two SAT solvers.

arXiv (Cornell University)
Limits and Structures in Graph Theory
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon