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A Critical Point For Random Graphs With A Given Degree Sequence (2000)
by
Michael Molloy
,
Bruce Reed
| Citations: | 506 - 8 self |
BibTeX
@MISC{Molloy00acritical,
author = {Michael Molloy and Bruce Reed},
title = {A Critical Point For Random Graphs With A Given Degree Sequence},
year = {2000}
}
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Abstract
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other well-known models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
