Lower Bounds for Book Ramsey Numbers

Abstract: We prove new bounds for Ramsey numbers for book graphs $B_n$. In particular, we show that $R(B_{n-1},B_n) = 4n-1$ for an infinite family of $n$ using a block-circulant construction similar to Paley graphs. We obtain improved bounds for several other values of $R(B_r,B_s)$ using different block-circulant graphs from SAT and integer programming (IP) solvers. Finally, we enumerate the number of critical graphs for $R(B_r,B_s)$ for small $r$ and $s$ using SAT modulo symmetries (SMS).