Counting Connected Graphs Asymptotically

Remco van der Hofstad; Joel Spencer

Counting Connected Graphs Asymptotically

组合数学 2007-05-23 v1 概率论

作者: Remco van der Hofstad , Joel Spencer

摘要

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

关键词

random graphs graph theory graph connectivity

引用

@article{arxiv.math/0502579,
  title  = {Counting Connected Graphs Asymptotically},
  author = {Remco van der Hofstad and Joel Spencer},
  journal= {arXiv preprint arXiv:math/0502579},
  year   = {2007}
}

备注

23 pages

Counting Connected Graphs Asymptotically

摘要

关键词

引用

备注

相关论文