• Publications
  • Influence
Random Graphs
Modern Graph Theory
  • B. Bollobás
  • Computer Science, Mathematics
  • Graduate Texts in Mathematics
  • 2002
TLDR
This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory. Expand
A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs
  • B. Bollobás
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • 1 December 1980
TLDR
The method determines the asymptotic distribution of the number of short cycles in graphs with a given degree sequence, and gives analogous formulae for hypergraphs. Expand
The phase transition in inhomogeneous random graphs
The “classical” random graph models, in particular G(n,p), are “homogeneous,” in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in theExpand
The degree sequence of a scale-free random graph process
TLDR
Here the authors obtain P(d) asymptotically for all d≤n1/15, where n is the number of vertices, proving as a consequence that γ=3.9±0.1 is obtained. Expand
The Diameter of a Scale-Free Random Graph
We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probabilityExpand
On generalized graphs
The phase transition in inhomogeneous random graphs
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scalingExpand
Extremal problems in graph theory
  • B. Bollobás
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1 June 1977
The aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
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