English

The size of bipartite graphs with girth eight

Combinatorics 2007-05-23 v1

Abstract

Reiman produced a quadratic inequality for the size of bipartite graphs of girth six. We get its counterpart for girth eight, a cubic inequality. It is optimal in as far as it admits the algebraic structure of generalized quadrangles as case of equality. This enables us to obtain the optimal estimate e ~ v^(4/3) for balanced bipartite graphs. We also get an optimal estimate for very unbalanced graphs.

Keywords

Cite

@article{arxiv.math/0102210,
  title  = {The size of bipartite graphs with girth eight},
  author = {Stefan Neuwirth},
  journal= {arXiv preprint arXiv:math/0102210},
  year   = {2007}
}

Comments

10 pages