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Degree distribution in random planar graphs

2008
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Discrete Mathematics & Theoretical Computer Science
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International audience We prove that for each $k \geq 0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, and moreover that $\sum_k d_k =1$. The proof uses the tools developed by Gimènez and Noy in their solution to the problem of the asymptotic enumeration of planar graphs, and is based on a detailed analysis of the generating functions involved in counting planar graphs. However, in order to keep track of the degree of the root,

doi:10.46298/dmtcs.3562
fatcat:ik3trguefvatviqxyy2juaqlzi