A tight lower bound on the maximum genus of a 3-connected loopless multigraph (Q1595254)
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scientific article; zbMATH DE number 1563600
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A tight lower bound on the maximum genus of a 3-connected loopless multigraph |
scientific article; zbMATH DE number 1563600 |
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A tight lower bound on the maximum genus of a 3-connected loopless multigraph (English)
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11 February 2001
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Let \(B(G)\) denote the cycle rank of a graph \(G\). The authors show that every 3-connected loopless multigraph \(G\) with \(B(G)< 10\) is upper-imbeddable; if \(B(G)\geq 10\), then the maximum genus of \(G\) is at least \(B(G)/3+ 1\). The lower bound is tight: there are infinitely many 3-connected loopless multigraphs attaining this bound.
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loopless multigraph
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maximum genus
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lower bound
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