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arXiv · 2410.03625

Lower Bounds for Book Ramsey Numbers

William J. Wesley
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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).

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William J. Wesley. 2025-09-04. Lower Bounds for Book Ramsey Numbers. https://doi.org/10.1016/j.disc.2025.114913

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