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| Content Provider | ACM Digital Library |
|---|---|
| Author | Panagiotou, Konstantinos Steger, Angelika |
| Abstract | Let $P_{n}$ be the class of all planar graphs with n labeled vertices, and let $P_{n}$ be a graph drawn uniformly at random from $P_{n}.$ In this paper we study the degree sequence of $P_{n}.$ We show that with probability 1 -- o(1) the number of vertices of degree k in $P_{n}$ is very close to a quantity $μ_{k}n$ that we determine explicitly, for all k ≤ c log n and an appropriate c > 0. A similar statement is true for random biconnected planar graphs as well. The main tool in our analysis is a framework that allows us under certain conditions to derive universal results about the degree distribution of random graphs from general classes with structural constraints. In particular, we address so-called critical graph classes, which due to their intricate structure have posed significant technical difficulties in the past. |
| Starting Page | 1198 |
| Ending Page | 1210 |
| Page Count | 13 |
| File Format | |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2011-01-23 |
| Access Restriction | Subscribed |
| Content Type | Text |
| Resource Type | Article |
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