论文标题
拉姆西的数字有规定的增长率
Ramsey numbers with prescribed rate of growth
论文作者
论文摘要
令$ r（g）$为图$ g $的两色拉姆齐号。在本说明中，我们证明，对于任何非删除函数$ n \ leq f（n）\ leq r（k_n）$，存在一系列连接的图形$（g_n）_ {n \ in \ mathbb n} $，带有$ | v（g_n）| = n $ for las $ n \ geq 1 $，因此$ r（g_n）=θ（f（n））$。相比之下，我们还表明，与均匀性的超图不一致至少$ 5 $。 我们还使用我们的技术来回答Debiasio提出的有关图形序列的存在，其$ 2 $ - 颜色的Ramsey数字是线性的，而其$ 3 $ -Colour Ramsey Number的$ 3 $ -Colour Ramsey Number具有超级线性的增长。
Let $R(G)$ be the two-colour Ramsey number of a graph $G$. In this note, we prove that for any non-decreasing function $n \leq f(n) \leq R(K_n)$, there exists a sequence of connected graphs $(G_n)_{n\in\mathbb N}$, with $|V(G_n)| = n$ for all $n \geq 1$, such that $R(G_n) = Θ(f(n))$. In contrast, we also show that an analogous statement does not hold for hypergraphs of uniformity at least $5$. We also use our techniques to answer a question posed by DeBiasio about the existence of sequences of graphs whose $2$-colour Ramsey number is linear whereas their $3$-colour Ramsey number has superlinear growth.
