Lower Bounds for Book Ramsey Numbers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915691862425600 |
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| author | Wesley, William J. |
| author_facet | Wesley, William J. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for Book Ramsey Numbers Wesley, William J. Combinatorics 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). |
| title | Lower Bounds for Book Ramsey Numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.03625 |