The Property of Having a $k$-Regular Subgraph Has a Sharp Threshold

Shoham Letzter

The Property of Having a $k$-Regular Subgraph Has a Sharp Threshold

Probability 2013-10-22 v1 Discrete Mathematics Combinatorics

Authors: Shoham Letzter

Abstract

We prove that the property of containing a $k$ -regular subgraph in the random graph model $G(n,p)$ has a sharp threshold for $k\ge3$ . We also show how to use similar methods to obtain an easy prove for the (known fact of) sharpness of having a non empty $k$ -core for $k\ge3$ .

Keywords

random graphs graph theory hypergraph theory

Cite

@article{arxiv.1310.5141,
  title  = {The Property of Having a $k$-Regular Subgraph Has a Sharp Threshold},
  author = {Shoham Letzter},
  journal= {arXiv preprint arXiv:1310.5141},
  year   = {2013}
}

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