The Ramsey number Rx(p, q) for a class of graphs X is the minimum n such that every graph in X with at least n vertices has either a clique of size p or an independent set of size q. We say that Ramsey number is linear in X if there is a constant k such that R_x (p, q) ≤ k(p+q) for all p, q. In the present paper we conjecture that Ramsey number is linear in X if and only if the co-chromatic number is bounded in X and determine Ramsey numbers for several classes of graphs that verify the conjecture.
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机译：一类图形X的Ramsey Number Rx（P，Q）是最小n，使得具有至少n个顶点的X中的每个图形具有尺寸P的Clique或独立的大小Q。我们说Ramsey号码在X中是线性的，如果存在常数k，使得所有P，Q的r_x（p，q）≤k（p + q）。在本文中，我们猜测Ramsey号码在X中是线性的，如果共结合数量界定在x中并确定验证猜想的几类图形的RAMSEY号码。
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