On the isometric embedding of arbitrary graphs into a graph of given diameter having the metric extension property (Q2760692)
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scientific article; zbMATH DE number 1682234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the isometric embedding of arbitrary graphs into a graph of given diameter having the metric extension property |
scientific article; zbMATH DE number 1682234 |
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13 December 2001
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graph
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distance
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metric
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metric extension property
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On the isometric embedding of arbitrary graphs into a graph of given diameter having the metric extension property (English)
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The metric extension property (MEP) for graphs means that every two vertices lie on a diametrical path. In 1988, \textit{A.~A.~Evdokimov} [Tr. Inst. Mat. 10, 116-132 (1988; Zbl 0676.94019)] asked: (1) Is it true that each graph \(G\) lies as an induced subgraph in a graph \(H\) that has the MEP? (2) Provided that \(G\) is connected, can it be embedded isometrically, i.e., preserving in \(H\) all the distances between vertices in \(G\)? The article under review answers both these questions in the positive.
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