Connectivity for Bridge-Addable Monotone Graph Classes

@article{AddarioBerry2012ConnectivityFB,
  title={Connectivity for Bridge-Addable Monotone Graph Classes},
  author={L. Addario-Berry and C. McDiarmid and B. Reed},
  journal={Comb. Probab. Comput.},
  year={2012},
  volume={21},
  pages={803-815}
}
  • L. Addario-Berry, C. McDiarmid, B. Reed
  • Published 2012
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • A class of labelled graphs is bridge-addable if, for all graphs G in and all vertices u and v in distinct connected components of G, the graph obtained by adding an edge between u and v is also in ; the class is monotone if, for all G ∈ and all subgraphs H of G, we have H ∈ . We show that for any bridge-addable, monotone class whose elements have vertex set {1,.i¾ .i¾ .,n}, the probability that a graph chosen uniformly at random from is connected is at least (1-on(1))e-i¾½, where on(1) → 0 as… CONTINUE READING

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