Infinite partitions of random graphs
β Scribed by Vojkan Vuksanovic
- Book ID
- 108167151
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 298 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Given an infinite graph G, let deg,(G) be defined as the smallest d for which V(G) can be partitioned into finite subsets of (uniformly) bounded size such that each part is adjacent to at most d others. A countable graph G is constructed with de&(G) > 2 and with the property that [{y~V(G):d(x, y)sn}
Let G be an infinite graph; define de& G to be the least m such that any partition P of the vertex set of G into sets of uniformly bounded cardinality contains a set which is adjacent to at least m Other sets of the partition. If G is either a regular tree 01 a triangtiisr, sqzart or hexagonal plana
Consider the general partitioning (GP) problem defined as follows: Partition the vertices of a graph into k parts W 1 W k satisfying a polynomial time verifiable property. In particular, consider properties (introduced by T. Feder, P. Hell, S. Klein, and R. Motwani, in "Proceedings of the Annual ACM