منابع مشابه
The Diameter of Random Graphs
Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
متن کاملOn the Diameter of Random Planar Graphs
We show that the diameter D(Gn) of a random labelled connected planar graph with n vertices is asymptotically almost surely of order n1/4, in the sense that there exists a constant c > 0 such that P (D(Gn) ∈ (n1/4− , n )) ≥ 1− exp(−n ) for small enough and n large enough (n ≥ n0( )). We prove similar statements for rooted 2-connected and 3-connected maps and planar graphs.
متن کاملThe Diameter of Sparse Random Graphs
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 log n log(np) if np → ∞. Moreover if np log n = c > 8, then the di...
متن کاملOn the Diameter of Hyperbolic Random Graphs
Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing performs close to optimal (Boguná, Papadopoulos, and Krioukov. Nature Communications, 1:62, 2010). This observation pushed the interest in hyperbolic networks as...
متن کاملThe Diameter of Random Sparse Graphs
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 >...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1981-0621971-7