Exhaustive Nonexistence of Circulant Ramsey(5,5;42/43) Colorings and Exploratory Symmetry-Constrained Search

Abstract

We exhaustively exclude ordinary circulant Ramsey(5,5;42) and Ramsey(5,5;43) colorings. We also report exploratory symmetry-constrained and unconstrained tabu searches. Values 84 for K42 and 129 for K43 are the best values produced by the stated runs, not literature records or proved global minima. Version 2 corrects the Version 1 neighborhood argument: a red neighborhood is Ramsey(4,5), not Ramsey(4,4), giving 17 ≤ d_red(v), d_blue(v) ≤ 24 for n = 42. Additional corrections and validation details are provided in CORRECTIONS.md and VALIDATION.md.