Graphs and Combinatorics

, Volume 27, Issue 1, pp 87–107 | Cite as

Random Planar Graphs with Bounds on the Maximum and Minimum Degrees

  • Chris DowdenEmail author
Original Paper


Let P n,d,D denote the graph taken uniformly at random from the set of all labelled planar graphs on {1, 2, . . . , n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability that P n,d,D will contain given components and subgraphs, showing exactly when this is bounded away from 0 and 1 as n → ∞.


Planar graphs Random graphs Bounded degrees Labelled graphs 

Mathematics Subject Classification (2000)

05C10 05C80 05C07 


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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.LIX, École PolytechniquePalaiseau CedexFrance

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