Partition theorems for parameter systems and graphs
✍ Scribed by H.J. Prőmel; B. Voigt
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 802 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
By means of a new combinatorial
structure-parameter systems-we prove that the class of finite ordered graphs has the partition property with respect to each object.
📜 SIMILAR VOLUMES
We study vertex partitions of graphs according to some minormonotone graph parameters. Ding et al. [J Combin Theory Ser B 79(2) (2000), 221-246] proved that some minor-monotone parameters are such that, any graph G with (G) ≥ 2 admits a vertex partition into two graphs with parameter at most (G)-1.
We prove a Ramsey-style theorem for sequences of vectors in an infinite-dimensional vector space over a finite field. As an application of this theorem, we prove that there are countably infinite Abelian groups whose Bohr topologies are not homeomorphic.