TY - JOUR
AU - Duggan, Conor
AU - Li, Zhengyu
AU - Bright, Curtis
AU - Ganesh, Vijay
PY - 2024/03/24
Y2 - 2024/07/17
TI - A SAT + Computer Algebra System Verification of the Ramsey Problem R(3, 8) (Student Abstract)
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 38
IS - 21
SE - AAAI Student Abstract and Poster Program
DO - 10.1609/aaai.v38i21.30437
UR - https://ojs.aaai.org/index.php/AAAI/article/view/30437
SP - 23480-23481
AB - The Ramsey problem R(3,8) asks for the smallest n such that every red/blue coloring of the complete graph on n vertices must contain either a blue triangle or a red 8-clique. We provide the first certifiable proof that R(3,8) = 28, automatically generated by a combination of Boolean satisfiability (SAT) solver and a computer algebra system (CAS). This SAT+CAS combination is significantly faster than a SAT-only approach. While the R(3,8) problem was first computationally solved by McKay and Min in 1992, it was not a verifiable proof. The SAT+CAS method that we use for our proof is very general and can be applied to a wide variety of combinatorial problems.
ER -