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}
}
• Published 2016
• Computer Science, Mathematics
• ArXiv
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
• Mathematics
• 1984
• 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
• Computer Science, Mathematics
• TALG
• 2010
• 34
• Highly Influential
Random 2 XORSAT Phase Transition
• Computer Science
• Algorithmica
• 2009
• 12
• PDF
The first cycles in an evolving graph
• Computer Science, Mathematics
• Discret. Math.
• 1989
• 122
• PDF