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
On the thickness of graphs of given degree
β Scribed by John H. Halton
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 940 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0020-0255
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## Abstract We prove that every connected graph __G__ contains a tree __T__ of maximum degree at most __k__ that either spans __G__ or has order at least __k__Ξ΄(__G__) + 1, where Ξ΄(__G__) is the minimum degree of __G.__ This generalizes and unifies earlier results of Bermond [1] and Win [7]. We als
The maximum number of cutvertices in a connected graph of order n having minimum degree at least 6 is determined for 6 > 5.
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