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Abstract
For a fixed degree sequence D = (d1, ..., dn), let G(D) be a uniformly chosen (simple) graph on {1, ..., n} where the vertex i has degree di. In this paper we determine whether G(D) has a giant component with high probability, essentially imposing no conditions on D. We simply insist that the sum of the degrees in D which are not 2 is at least λ(n) for some function λ going to infinity with n. This is a relatively minor technical condition, and when D does not satisfy it, both the probability that G(D) has a giant component and the probability that G(D) has no giant component are bounded away from 1.
Original language | English |
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Pages (from-to) | 263-310 |
Number of pages | 48 |
Journal | Probability Theory and Related Fields |
Volume | 170 |
Issue number | 1-2 |
Early online date | 26 Jan 2017 |
DOIs | |
Publication status | Published - Feb 2018 |
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Dive into the research topics of 'How to determine if a random graph with a fixed degree sequence has a giant component'. Together they form a unique fingerprint.Projects
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Randomized approaches to combinatorIal packing and covering problems
Kuhn, D. (Principal Investigator) & Osthus, D. (Co-Investigator)
Engineering & Physical Science Research Council
1/03/15 → 28/02/18
Project: Research Councils