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
Independent finite sums in graphs defined on the natural numbers
✍ Scribed by Tomasz Luczak; Vojtěch Rödl; Tomasz Schoen
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 281 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0012-365X
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