Authors
Citation
Ds. Gunderson et al., Independent arithmetic progressions in clique-free graphs on the natural numbers, J COMB TH A, 93(1), 2001, pp. 1-17
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165
→ ACNP
Volume
93
Issue
1
Year of publication
2001
Pages
1 - 17
Database
ISI
SICI code
0097-3165(200101)93:1<1:IAPICG>2.0.ZU;2-Y
Abstract
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 i
ts difference. This is a common generalization of theorems of Schur, van de
r Waerden, and Ramsey. We also discuss various related questions regarding
(m, p, c)-sets and parameter words. (C) 2001 Academic Press.