The Bohman-Frieze process near criticality

@article{Kang2013TheBP,
  title={The Bohman-Frieze process near criticality},
  author={Mihyun Kang and Will Perkins and J. Spencer},
  journal={Random Struct. Algorithms},
  year={2013},
  volume={43},
  pages={221-250}
}
  • Mihyun Kang, Will Perkins, J. Spencer
  • Published 2013
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • The Erd\H{o}s-R\'{e}nyi process begins with an empty graph on n vertices and edges are added randomly one at a time to a graph. A classical result of Erd\H{o}s and R\'{e}nyi states that the Erd\H{o}s-R\'{e}nyi process undergoes a phase transition, which takes place when the number of edges reaches n/2 (we say at time 1) and a giant component emerges. Since this seminal work of Erd\H{o}s and R\'{e}nyi, various random graph models have been introduced and studied. In this paper we study the so… CONTINUE READING
    20 Citations
    Bohman-Frieze processes at criticality and emergence of the giant component
    • 5
    • Highly Influenced
    • PDF
    Pursuing the Giant in Random Graph Processes
    • 1
    • PDF
    The evolution of subcritical Achlioptas processes
    • 16
    • PDF
    Some asymptotic problems for dynamical random graphs
    Convergence of Achlioptas Processes via Differential Equations with Unique Solutions
    • 7
    • PDF
    Bounded-Size Rules: The Barely Subcritical Regime
    • 7
    • Highly Influenced
    • PDF
    On the largest component in the subcritical regime of the Bohman-Frieze process
    • 4
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 48 REFERENCES
    Bohman-Frieze processes at criticality and emergence of the giant component
    • 5
    • PDF
    Birth control for giants
    • 99
    • PDF
    Hamiltonicity thresholds in Achlioptas processes
    • 36
    • PDF
    The triangle-free process
    • 127
    • PDF
    Component behavior near the critical point of the random graph process
    • 147
    • Highly Influential
    The early evolution of the H-free process
    • 145
    • PDF
    Component Behavior Near the Critical Point of the Random Graph Process
    • T. Luczak
    • Computer Science
    • Random Struct. Algorithms
    • 1990
    • 149
    Two critical periods in the evolution of random planar graphs
    • 27
    • PDF
    Avoiding small subgraphs in Achlioptas processes
    • 13
    • PDF