Lower bounds for book Ramsey numbers

We prove new bounds for Ramsey numbers for book graphs B n . In particular, we show that R ( B n − 1 , B n ) = 4 n − 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).