Clusters in a multigraph with elevated density (Q870066)
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scientific article; zbMATH DE number 5132844
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Clusters in a multigraph with elevated density |
scientific article; zbMATH DE number 5132844 |
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Clusters in a multigraph with elevated density (English)
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12 March 2007
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Summary: In this paper, we prove that in a multigraph whose density \(\Gamma\) exceeds the maximum vertex degree \(\Delta\), the collection of minimal clusters (maximally dense sets of vertices) is cycle-free. We also prove that for multigraphs with \(\Gamma > \Delta + 1\), the size of any cluster is bounded from the above by \((\Gamma - 3)/ (\Gamma - \Delta -1)\). Finally, we show that two well-known lower bounds for the chromatic index of a multigraph are equal.
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0.7715572714805603
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0.7636615037918091
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0.7586512565612793
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0.7575141191482544
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