Asymptotic Study of Subcritical Graph Classes

@article{Drmota2011AsymptoticSO,
  title={Asymptotic Study of Subcritical Graph Classes},
  author={Michael Drmota and {\'E}ric Fusy and Mihyun Kang and Veronika Kraus and Juanjo Ru{\'e}},
  journal={SIAM J. Discret. Math.},
  year={2011},
  volume={25},
  pages={1615-1651}
}
  • Michael Drmota, Éric Fusy, +2 authors Juanjo Rué
  • Published in SIAM J. Discret. Math. 2011
  • Mathematics, Computer Science
  • We present a unified general method for the asymptotic study of graphs from the so-called subcritical graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works in both the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp., $g_n$) of labelled (resp., unlabelled… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 39 REFERENCES

    Singularity Analysis of Generating Functions

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Analytic Combinatorics

    VIEW 7 EXCERPTS
    HIGHLY INFLUENTIAL

    Two-connected graphs with prescribed three-connected components

    VIEW 6 EXCERPTS
    HIGHLY INFLUENTIAL

    Combinatorial species and tree-like structures

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Systems of functional equations

    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Degree distribution in random planar graphs

    VIEW 1 EXCERPT