The Diameter of Random Sparse Graphs
نویسندگان
چکیده
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) equals (1 + o(1)) log n log(np) if np → ∞. Moreover if np log n = c > 8, then the diameter of G(n, p) is concentrated on two values. In general, if np 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.
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