Chromatically unique multibridge graphs (Q1422157)
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scientific article; zbMATH DE number 2038358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chromatically unique multibridge graphs |
scientific article; zbMATH DE number 2038358 |
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Chromatically unique multibridge graphs (English)
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5 February 2004
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Summary: Let \(\theta (a_1,a_2,\dots ,a_k)\) denote the graph obtained by connecting two distinct vertices with \(k\) independent paths of lengths \(a_1,a_2, \dots ,a_k\) respectively. Assume that \(2\leq a_1\leq a_2\leq \cdots \leq a_k\). We prove that the graph \(\theta (a_1,a_2, \dots ,a_k)\) is chromatically unique if \(a_k < a_1+a_2\), and find examples showing that \(\theta (a_1,a_2, \dots ,a_k)\) may not be chromatically unique if \(a_k=a_1+a_2\).
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chromatic polynomials
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polygon-tree
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