We show that if G is a K-r-free graph on N. there is an independent set in G which contains an arbitrarily long arithmetic progression together with its difference. This is a common generalization of theorems of Schur, van der Waerden, and Ramsey. We also discuss various related questions regarding (m, p, c)-sets and parameter words. (C) 2001 Academic Press. [References: 18]
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机译：我们表明，如果G是N上无K-r的图，则G中有一个独立的集合，其中包含任意长的算术级数及其差。这是Schur，van der Waerden和Ramsey定理的普遍概括。我们还将讨论有关（m，p，c）-集和参数字的各种相关问题。 （C）2001学术出版社。 [参考：18]
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