- Abstract:
- Let the random graph Rn be drawn uniformly at random from the set of all simple planar graphs on n labelled vertices. We see that with high probability the maximum degree of Rn is ⊖(ln n). We consider also the maximum size of a face and the maximum increase in the number of components on deleting a vertex. These results extend to graphs embeddable on any fixed surface. © 2008 Cambridge University Press.
- Publication status:
- Published
- Publisher copy:
- 10.1017/S0963548308009097
-
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- Journal:
- Combinatorics, Probability and Computing
- Volume:
- 17
- Issue:
- 4
- Pages:
- 591-601
- Publication date:
- 2008
- DOI:
- EISSN:
-
1469-2163
- ISSN:
-
0963-5483
- URN:
-
uuid:5f097513-a439-4815-bdb5-e147feeb7b02
- Source identifiers:
-
102285
- Local pid:
- pubs:102285
- Language:
- English
- Copyright date:
- 2008
Journal article
On the Maximum Degree of a Random Planar Graph.
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