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The diameter of sparse random graphs (2001)
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| Venue: | ADV. IN APPL. MATH |
| Citations: | 52 - 1 self |
BibTeX
@ARTICLE{Chung01thediameter,
author = {Fan Chung and Linyuan Lu},
title = {The diameter of sparse random graphs},
journal = {ADV. IN APPL. MATH},
year = {2001},
volume = {26},
pages = {2001}
}
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Abstract
We consider the diameter of a random graph G�n � p � for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of random graph log n G�n � p � is close to if np →∞. Moreover if = c>8, then the diameter log�np� np of G�n � p � is concentrated on two values. In general, if log n = c>c0, the diameter is concentrated on at most 2�1/c0�+4 values. We also proved that the diameter of G�n � p � is almost surely equal to the diameter of its giant component if np > 3.6.
