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  • Isolated cycles of critical random graphs 

    Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Society for Industrial and Applied Mathematics (SIAM), 2017)
    Conference report
    Open Access
    Consider the Erdos-Renyi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of n2 edges. Let L be a set of positive integers. For any number of edges M 6n/2 + O(n 2/3 ), we compute ...
  • On the probability of planarity of a random graph near the critical point 

    Noy Serrano, Marcos; Ravelomanana, Vlady; Rue, Juanjo (2015-03-01)
    Open Access
    Let G(n, M) be the uniform random graph with n vertices and M edges. Erdos and Renyi (1960) conjectured that the limiting probability; lim(n ->infinity) Pr{G(n, n/2) is planar}; exists and is a constant strictly between 0 ...