Corpus ID: 9249131

The Maximum Block Size of Critical Random Graphs

@article{Rasendrahasina2016TheMB,
  title={The Maximum Block Size of Critical Random Graphs},
  author={Vonjy Rasendrahasina and A. Rasoanaivo and V. Ravelomanana},
  journal={ArXiv},
  year={2016},
  volume={abs/1605.04340}
}
Let $G(n,\, M)$ be the uniform random graph with $n$ vertices and $M$ edges. Let $B_n$ be the maximum block-size of $G(n,\, M)$ or the maximum size of its maximal $2$-connected induced subgraphs. We determine the expectation of $B_n$ near the critical point $M=n/2$. As $n-2M \gg n^{2/3}$, we find a constant $c_1$ such that \[ c_1 = \lim_{n \rightarrow \infty} \left(1 - \frac{2M}{n} \right) \, E B_n \, . \] Inside the window of transition of $G(n,\, M)$ with $M=\frac{n}{2}(1+\lambda n^{-1/3… Expand

References

SHOWING 1-10 OF 30 REFERENCES
On the evolution of random graphs
  • 5,510
  • Highly Influential
  • PDF
The number of connected sparsely edged graphs
  • E. Wright
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1977
  • 139
Maximal biconnected subgraphs of random planar graphs
  • 34
  • Highly Influential
Blocks in Constrained Random Graphs with Fixed Average Degree
  • 3
Random 2 XORSAT Phase Transition
  • 12
  • PDF
On the probability of planarity of a random graph near the critical point
  • 24
  • PDF
The first cycles in an evolving graph
  • 122
  • PDF
The number of connected sparsely edged graphs. III. Asymptotic results
  • E. Wright
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1980
  • 77
...
1
2
3
...