Counting connected graphs asymptotically

Remco van der Hofstad, Joel Spencer

Research output: Contribution to journalArticle

Abstract

We find the asymptotic number of connected graphs with k vertices and k - 1 + l edges when k, l approach infinity, re-proving a result of Bender, Canfield and McKay. We use the probabilistic method, analyzing breadth-first search on the random graph G (k, p) for an appropriate edge probability p. Central is the analysis of a random walk with fixed beginning and end which is tilted to the left.

Original languageEnglish (US)
Pages (from-to)1294-1320
Number of pages27
JournalEuropean Journal of Combinatorics
Volume27
Issue number8 SPEC. ISS.
DOIs
StatePublished - Nov 2006

Fingerprint

Breadth-first Search
Probabilistic Methods
Random Graphs
Connected graph
Counting
Random walk
Infinity

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Counting connected graphs asymptotically. / van der Hofstad, Remco; Spencer, Joel.

In: European Journal of Combinatorics, Vol. 27, No. 8 SPEC. ISS., 11.2006, p. 1294-1320.

Research output: Contribution to journalArticle

van der Hofstad, Remco ; Spencer, Joel. / Counting connected graphs asymptotically. In: European Journal of Combinatorics. 2006 ; Vol. 27, No. 8 SPEC. ISS. pp. 1294-1320.
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