Cycles And Unicyclic Components In Random Graphs

  • Svante Janson
  • Published 2003 in Combinatorics, Probability & Computing

Abstract

The sizes of the cycles and unicyclic components in the random graph G(n, n/2 ± s), where n ≪ s ≪ n, are studied using the language of point processes. This refines several earlier results by different authors. Asymptotic distributions of various random variables are given; these distributions include the gamma distributions with parameters 1/4, 1/2 and 3/4, as well as the Poisson–Dirichlet and GEM distributions with parameters 1/4 and 1/2.

DOI: 10.1017/S0963548302005412

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Cite this paper

@article{Janson2003CyclesAU, title={Cycles And Unicyclic Components In Random Graphs}, author={Svante Janson}, journal={Combinatorics, Probability & Computing}, year={2003}, volume={12}, pages={27-52} }