On the number of edges in random planar graphs

被引：26
|
作者：
Gerke, S
McDiarmid, A
机构：
[1] Tech Univ Munich, Inst Informat, D-80290 Munich, Germany
[2] Univ Oxford, Dept Stat, Oxford OX1 3TG, England
来源：
COMBINATORICS PROBABILITY & COMPUTING | 2004年 / 13卷 / 02期
关键词：
D O I：
10.1017/S0963548303005947
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We consider random planar graphs on n labelled nodes, and show in particular that if the graph is picked uniformly at random then the expected number of edges is at least 13/7n + o(n). To prove this result we give a lower bound on the size of the set of edges that can be added to a planar graph on n nodes and m edges while keeping it planar, and in particular we see that if m is at most 13/7n - c (for a suitable constant c) then at least this number of edges can be added.
引用
收藏
页码：165 / 183
页数：19
相关论文
共 50 条
  • [1] Random planar graphs with n nodes and a fixed number of edges
    Gerke, Stefanie
    McDiarmid, Colin
    Steger, Angelika
    Weissl, Andreas
    [J]. PROCEEDINGS OF THE SIXTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2005, : 999 - 1007
  • [2] Number of edges in inhomogeneous random graphs
    Zhishui Hu
    Liang Dong
    [J]. Science China Mathematics, 2021, 64 : 1321 - 1330
  • [3] Number of edges in inhomogeneous random graphs
    Zhishui Hu
    Liang Dong
    [J]. Science China Mathematics, 2021, 64 (06) : 1321 - 1330
  • [4] Number of edges in inhomogeneous random graphs
    Hu, Zhishui
    Dong, Liang
    [J]. SCIENCE CHINA-MATHEMATICS, 2021, 64 (06) : 1321 - 1330
  • [5] On random planar graphs, the number of planar graphs and their triangulations
    Osthus, D
    Prömel, HJ
    Taraz, A
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2003, 88 (01) : 119 - 134
  • [6] THE NUMBER OF EDGES IN k-QUASI-PLANAR GRAPHS
    Fox, Jacob
    Pach, Janos
    Suk, Andrew
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2013, 27 (01) : 550 - 561
  • [7] On the maximum number of edges in quasi-planar graphs
    Ackerman, Eyal
    Tardos, Gabor
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2007, 114 (03) : 563 - 571
  • [8] On the maximum number of edges in planar graphs of bounded degree and matching number
    Jaffke, Lars
    Lima, Paloma T.
    [J]. DISCRETE MATHEMATICS, 2023, 346 (08)
  • [9] THE AUTOMORPHISM GROUP OF RANDOM GRAPHS WITH A GIVEN NUMBER OF EDGES
    LUCZAK, T
    [J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 104 : 441 - 449
  • [10] Quasi-planar graphs have a linear number of edges
    Agarwal, PK
    Aronov, B
    Pach, J
    Pollack, R
    Sharir, M
    [J]. GRAPH DRAWING, 1996, 1027 : 1 - 7
12345