Lower Bounds for Book Ramsey Numbers
Abstract
We prove new bounds for Ramsey numbers for book graphs Bn. In particular, we show that R(Bn-1,Bn) = 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(Br,Bs) using different block-circulant graphs from SAT and integer programming (IP) solvers. Finally, we enumerate the number of critical graphs for R(Br,Bs) for small r and s using SAT modulo symmetries (SMS).
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