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}
}
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10 pages