PreprintarXiv licencearXiv
An upper bound of 61 for the Ramsey number $R(3,3,3,3)$
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.
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BibTeX
@misc{tatarevic2026upper,
title = {{An upper bound of 61 for the Ramsey number $R(3,3,3,3)$}},
author = {Milos Tatarevic},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36648},
eprint = {2610.36648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36648},
}
RIS
TY - UNPB
TI - An upper bound of 61 for the Ramsey number $R(3,3,3,3)$
AU - Milos Tatarevic
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36648
UR - https://arxiv.org/abs/2610.36648
AB - 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.
ER -