Extremal Parameters in Sub-Critical Graph Classes

We analyze several extremal parameters like the diameter or the maximum degree in sub-critial graph classes. Subcritical graph classes cover several well-known classes of graphs like trees, outerplanar graph or series-parallel graphs which have been intensively studied during the last few years. However, this paper is the first one, where these kinds of parameters are studied from a general point of view.

[1]  Philippe Flajolet,et al.  The Average Height of Binary Trees and Other Simple Trees , 1982, J. Comput. Syst. Sci..

[2]  M. Drmota Random Trees: An Interplay between Combinatorics and Probability , 2009 .

[3]  Michael Drmota,et al.  A Bivariate Asymptotic Expansion of Coefficients of Powers of Generating Functions , 1994, Eur. J. Comb..

[4]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[5]  Edward A. Bender,et al.  The Number of Degree-Restricted Rooted Maps on the Sphere , 1994, SIAM J. Discret. Math..

[6]  Michael Drmota,et al.  Predecessors in Random Mappings , 1996, Comb. Probab. Comput..

[7]  Gilbert Labelle,et al.  Combinatorial species and tree-like structures , 1997, Encyclopedia of mathematics and its applications.

[8]  Marc Noy,et al.  Vertices of given degree in series‐parallel graphs , 2010, Random Struct. Algorithms.

[9]  Guy Louchard,et al.  Boltzmann Samplers for the Random Generation of Combinatorial Structures , 2004, Combinatorics, Probability and Computing.

[10]  Marc Noy,et al.  The Maximum Degree of Series-Parallel Graphs , 2011, Combinatorics, Probability and Computing.

[11]  Marc Noy,et al.  Vertices of given degree in series-parallel graphs , 2010 .

[12]  Jerzy Jaworski Predecessors in a random mapping , 1998, Random Struct. Algorithms.

[13]  Philippe Flajolet,et al.  Singularity Analysis of Generating Functions , 1990, SIAM J. Discret. Math..

[14]  Konstantinos Panagiotou,et al.  The Degree Sequence of Random Graphs from Subcritical Classes† , 2009, Combinatorics, Probability and Computing.

[15]  Michael Drmota,et al.  Asymptotic Study of Subcritical Graph Classes , 2010, SIAM J. Discret. Math..