{"id":"hexagon/2610.00455","pdf":"https://hexagonmath.org/pdf/2610.00455v1","url":"https://hexagonmath.org/abs/2610.00455v1","tags":["msc:05C55","msc:05C25","msc:05B10","Ramsey number","block-circulant graph","book graph","formal verification","local search"],"score":0,"title":"The book Ramsey number $R(B_{57},B_{58})=231$","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.CO","summary":"We construct a graph on $230$ vertices with no book $B_{57}$ whose complement contains no $B_{58}$. With the upper bound of Rousseau and Sheehan this gives $R(B_{57},B_{58})=231$, the smallest case of Wesley's conjecture $R(B_{n-1},B_n)=4n-1$ that was open. The graph is a two-block circulant graph over $\\Z_{115}$, and the proof reduces to $57$ inequalities.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}