Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree (Q2712593)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree |
scientific article |
Statements
17 February 2002
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graph minor
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crossing number
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Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree (English)
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The authors firstly show that if a graph \(G\) has a minor \(M\) with the maximum degree of vertices at most 4, then the crossing number of \(G\) in a surface \(\Sigma\) is at least one fourth the crossing number of \(M\) in \(\Sigma\). Further, based on this result, they find that every graph embedded in the torus with representativity \(r\geq 6\) has Klein bottle crossing number at least \(\lfloor 2r/3\rfloor^2/64\).
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