The size of bipartite graphs with girth eight
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.
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