On the size of a random maximal graph
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On random planar graphs, the number of planar graphs and their triangulations
Journal of Combinatorial Theory Series B
On the Number of Edges in Random Planar Graphs
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series B
Random planar graphs with n nodes and a fixed number of edges
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Generating unlabeled connected cubic planar graphs uniformly at random
Random Structures & Algorithms
On the random satisfiable process
Combinatorics, Probability and Computing
Ant colony optimization and the minimum cut problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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We consider the following variant of the classical random graph process introduced by Erdős and Rényi. Starting with an empty graph on n vertices, choose the next edge uniformly at random among all edges not yet considered, but only insert it if the graph remains planar. We show that for all ε 0, with high probability, &thetas;(n2) edges have to be tested before the number of edges in the graph reaches (1 + ε)n. At this point, the graph is connected with high probability and contains a linear number of induced copies of any fixed connected planar graph, the first property being in contrast and the second one in accordance with the uniform random planar graph model. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008