An extremal characterization of projective planes (Q1010880)
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scientific article; zbMATH DE number 5541048
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extremal characterization of projective planes |
scientific article; zbMATH DE number 5541048 |
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An extremal characterization of projective planes (English)
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7 April 2009
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Summary: We prove that amongst all \(n\) by \(n\) bipartite graphs of girth at least six, where \(n = q^2 + q + 1 \geq 157\), the incidence graph of a projective plane of order \(q\), when it exists, has the maximum number of cycles of length eight. This characterizes projective planes as the partial planes with the maximum number of quadrilaterals.
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bipartite graphs
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incidence graph
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projective plane
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maximum number of cycles
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number of quadrilaterals
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