The critical phase for random graphs with a given degree sequence

被引：16
|
作者：
Kang, M. [1 ]
Seierstad, T. G. [1 ]
机构：
[1] Humboldt Univ, Inst Informat, D-10099 Berlin, Germany
来源：
COMBINATORICS PROBABILITY & COMPUTING | 2008年 / 17卷 / 01期
关键词：
Graph theory;
D O I：
10.1017/S096354830700867X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We consider random graphs with a fixed degree sequence. Molloy and Reed [11, 12] studied how the size of the giant component changes according to degree conditions. They showed that there is a phase transition and investigated the order of components before and after the critical phase. In this paper we study more closely the order of components at the critical phase, using singularity analysis of a generating function for a branching process which models the random graph with it given degree sequence.
引用
收藏
页码：67 / 86
页数：20
相关论文
共 50 条
  • [1] A CRITICAL-POINT FOR RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE
    MOLLOY, M
    REED, B
    [J]. RANDOM STRUCTURES & ALGORITHMS, 1995, 6 (2-3) : 161 - 179
  • [2] RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE
    Chatterjee, Sourav
    Diaconis, Persi
    Sly, Allan
    [J]. ANNALS OF APPLIED PROBABILITY, 2011, 21 (04): : 1400 - 1435
  • [3] Percolation on Sparse Random Graphs with Given Degree Sequence
    Fountoulakis, N.
    [J]. INTERNET MATHEMATICS, 2007, 4 (04) : 329 - 356
  • [4] The number of graphs and a random graph with a given degree sequence
    Barvinok, Alexander
    Hartigan, J. A.
    [J]. RANDOM STRUCTURES & ALGORITHMS, 2013, 42 (03) : 301 - 348
  • [5] Largest component of subcritical random graphs with given degree sequence*
    Coulson, Matthew
    Perarnau, Guillem
    [J]. ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28 : 1 - 28
  • [6] A novel configuration model for random graphs with given degree sequence
    Xu Xin-Ping
    Liu Feng
    [J]. CHINESE PHYSICS, 2007, 16 (02): : 282 - 286
  • [7] THE COMPONENT SIZES OF A CRITICAL RANDOM GRAPH WITH GIVEN DEGREE SEQUENCE
    Joseph, Adrien
    [J]. ANNALS OF APPLIED PROBABILITY, 2014, 24 (06): : 2560 - 2594
  • [8] Towards random uniform sampling of bipartite graphs with given degree sequence
    Miklos, Istvan
    Erdos, Peter L.
    Soukup, Lajos
    [J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2013, 20 (01):
  • [9] DEGREE SEQUENCE OF RANDOM PERMUTATION GRAPHS
    Bhattacharya, Bhaswar B.
    Mukherjee, Sumit
    [J]. ANNALS OF APPLIED PROBABILITY, 2017, 27 (01): : 439 - 484
  • [10] The cores of random hypergraphs with a given degree sequence
    Cooper, C
    [J]. RANDOM STRUCTURES & ALGORITHMS, 2004, 25 (04) : 353 - 375
12345