## Abstract Let __G__ be a graph on __n__ vertices in which every induced subgraph on ${s}={\log}^{3}\, {n}$ vertices has an independent set of size at least ${t}={\log}\, {n}$. What is the largest ${q}={q}{(n)}$ so that every such __G__ must contain an independent set of size at least __q__? This
On subgraph number independence in trees
✍ Scribed by R.L Graham; E Szemerédi
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 428 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
Let \_(n, m, k) be the largest number \_ # [0, 1] such that any graph on n vertices with independence number at most m has a subgraph on k vertices with at lest \_ } ( k 2 ) edges. Up to a constant multiplicative factor, we determine \_(n, m, k) for all n, m, k. For log n m=k n, our result gives \_(
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