The Number of Independent Sets in a Graph with Small Maximum Degree
โ Scribed by David Galvin; Yufei Zhao
- Publisher
- Springer Japan
- Year
- 2010
- Tongue
- English
- Weight
- 180 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Suppose that n i> 2t + 2 (t/> 17). Let G be a graph with n vertices such that its complement is connected and, for all distinct non-adjacent vertices u and v, there are at least t common neighbours. Then we prove that and Furthermore, the results are sharp.
A vertex x in a subset X of vertices of an undirected graph is redundant if its dosed neighborhood is contained in the union of closed neighborhoods of vertices of X-{x}. In the context of a communications network, this means that any vertex that may receive communications from X may also be irdorme
We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S
A subset of vertices is a maximum independent set if no two of the vertices are joined by an edge and the subset has maximum cardinality. In this paper we answer a question posed by Herb Wilf. We show that the greatest number of maximum independent sets for a tree of n vertices is 2(n-3\* for odd n