W. J. Wesley

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20242026

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math.CO2024

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$

Pavel Pudlák, Vojtěch Rödl, William J. Wesley

We will prove that $R_{k} (k + 1, k + 1) \geq 4 t w_{⌊ k /4 ⌋ - 3} (2)$ , where $tw$ is the tower function defined by $tw_{1} (x) = x$ and $tw_{i + 1} (x) = 2^{tw_{i} (x)}$ . We also give pro…

math.CO2024

Lower Bounds for Book Ramsey Numbers

William J. Wesley

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…

A lower bound on the Ramsey number Rk​(k+1,k+1)

Lower Bounds for Book Ramsey Numbers

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$