Asymptotic enumeration and limit laws of planar graphs

By Omer Giménez, M. Noy. 2005

174 citations recorded by the source corpus.

A graph is planar if it can be embedded in the plane, or in the sphere, so that no two edges cross at an interior point. A planar graph together with a particular embedding is called a map. There is a rich theory of counting maps, started by Tutte in the 1960's. However, in this paper we are interested in counting graphs as combinatorial objects, regardless of how many nonequivalent topological embeddings they may have. As we are going to see, this makes the counting considerably more difficult.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/47567dfc4db6beddd3d5b8f372c1d8bf8b735a1b

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

A simple solution to the k-core problem (2007, methodology): “approaches have been applied: the first is the probabilistic method [7, 8, 15, 22–24, 30, 32]; the second is based on connectivity decomposition and generating functions [1,3,5,7,9–12, 25, 29]; the third is the matrix integral method [6, 13, 14, 16, 17, 27].”