The Diameter of Sparse Random Graphs |
| |
Authors: | Fan Chung Linyuan Lu |
| |
Institution: | Department of Mathematics, University of California, San Diego, La Jolla, California, 92093 |
| |
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 G(n, p) is close to
if np → ∞. Moreover if
, then the diameter of G(n, p) is concentrated on two values. In general, if
, the diameter is concentrated on at most 21/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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|