On the crossing number of \(K_{m,n}\) (Q1408549)
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scientific article; zbMATH DE number 1985383
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the crossing number of \(K_{m,n}\) |
scientific article; zbMATH DE number 1985383 |
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On the crossing number of \(K_{m,n}\) (English)
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24 September 2003
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Summary: The best lower bound known on the crossing number of the complete bipartite graph is \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor.\) We prove that \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2\) for sufficiently large \(m\) and \(n\).
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