Partial cubes and their \(\tau\)-graphs (Q875040)
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scientific article; zbMATH DE number 5141655
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Partial cubes and their \(\tau\)-graphs |
scientific article; zbMATH DE number 5141655 |
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Partial cubes and their \(\tau\)-graphs (English)
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10 April 2007
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A partial cube graph is an isometric subgraph of a hypercube. On such graphs the Djoković-Winkler relation is an equivalence. The equivalence classes form the \(\tau\)-graph with edges corresponding to convex 3-node paths. It is shown that any graph is the \(\tau\)-graph of some median graph. The \(\tau\)-graph is connected only for Cartesian prime graphs. For a median graph it is \(K_n\)-free if and only if the original contains no convex star.
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partial cube
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convex path
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Djoković-Winkler relation
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median graph
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