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RANDOM SUBGRAPHS IN SPARSE GRAPHS.
- Source :
-
SIAM Journal on Discrete Mathematics . 2015, Vol. 29 Issue 4, p2350-2360. 11p. - Publication Year :
- 2015
-
Abstract
- We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solves the problem for Cartesian powers of arbitrary graphs. In detail, let G be a connected graph on k vertices, Gn be the nth Cartesian power of G, αi be the number of vertices of degree i of G, λ be a positive real number, and Gnp be the graph obtained from Gn by deleting every edge independently with probability 1 − p. If ∑i αi(1 − p)i = λ 1/n , then limn→∞ ℙ[Gnp is connected] = exp(−λ). This result extends known results for regular graphs. The main result implies that the threshold probability does not depend on the graph structure of G itself, but only on the degree sequence of the graph. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RANDOM graphs
*SUBGRAPHS
*SPARSE graphs
*GEOMETRIC vertices
*PROBABILITY theory
Subjects
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 29
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 117003460
- Full Text :
- https://doi.org/10.1137/140976340