This note can be treated a s a supplement to a paper written by Bollobas which was devoted to the vertices of a given degree in a random graph. We determine some values of the edge probability p for which the number of vertices of a given degree of a random graph G E ?An, p) asymptotically has a nor
Estimation of the number of vertices of different degrees in a graph
β Scribed by Ove Frank
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 971 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Albertson, M.O. and D.M. Berman, The number of cut-vertices in a graph of given minimum degree, Discrete Mathematics 89 (1991) 97-100. A graph with n vertices and minimum degree k 2 2 can contain no more than (2k -2)n/(kz -2) cut-vertices. This bound is asymptotically tight. \* Research supported in
For a connected graph G, let ~-(G) be the set of all spanning trees of G and let nd(G) be the number of vertices of maximum degree in G. In this paper we show that if G is a cactus or a connected graph with p vertices and p+ 1 edges, then the set {na(T) : T C ~-(G)) has at most one gap, that is, it