English

Infinite graphs that do not contain cycles of length four

Combinatorics 2016-01-25 v3 Number Theory

Abstract

We construct a countable infinite graph G that does not contain cycles of length four having the property that the sequence of graphs GnG_n induced by the first nn vertices has minimum degree δ(Gn)>n21+o(1)\delta(G_n)> n^{\sqrt{2}-1+o(1)}.

Keywords

Cite

@article{arxiv.1401.4502,
  title  = {Infinite graphs that do not contain cycles of length four},
  author = {Javier Cilleruelo},
  journal= {arXiv preprint arXiv:1401.4502},
  year   = {2016}
}

Comments

This paper has been withdrawn because we have found an easier proof of the result