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Independent Deuber sets in graphs on the natural numbers
- Source :
-
Journal of Combinatorial Theory - Series A . Aug2003, Vol. 103 Issue 2, p305. 18p. - Publication Year :
- 2003
-
Abstract
- We show that for any <f>k,m,p,c,</f> if <f>G</f> is a <f>Kk</f>-free graph on <f>N</f> then there is an independent set of vertices in <f>G</f> that contains an <f>(m,p,c)</f>-set. Hence if <f>G</f> is a <f>Kk</f>-free graph on <f>N</f>, then one can solve any partition regular system of equations in an independent set. This is a common generalization of partition regularity theorems of Rado (who characterized systems of linear equations <f>Ax=0</f> a solution of which can be found monochromatic under any finite coloring of <f>N</f>) and Deuber (who provided another characterization in terms of <f>(m,p,c)</f>-sets and a partition theorem for them), and of Ramsey''s theorem itself. [Copyright &y& Elsevier]
- Subjects :
- *SET theory
*RAMSEY theory
*GRAPH theory
Subjects
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 103
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 10424816
- Full Text :
- https://doi.org/10.1016/S0097-3165(03)00100-6