Many large eigenvalues in sparse graphs
โ Scribed by Mohar, Bojan
- Book ID
- 120335064
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 357 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract For a graph __G__, let __a__(__G__) denote the maximum size of a subset of vertices that induces a forest. Suppose that __G__ is connected with __n__ vertices, __e__ edges, and maximum degree ฮ. Our results include: (a) if ฮโโคโ3, and __G__โโ โ__K__~4~, then __a__(__G__)โโฅโ__n__โโโe/4โโโ1
Let k be a fixed positive integer. A graph H has property Mk if it contains [ยฝk] edge disjoint hamilton cycles plus a further edge disjoint matching which leaves at most one vertex isolated, if k is odd. Let p = c/n, where c is a large enough constant. We show that G,,p a.s. contains a vertex induce