Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes (Q2502966)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes |
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Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes (English)
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13 September 2006
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The author proves that for a graph \(G\), the neighborhood complex \(\mathcal N(G)\) and (the barycentric subdivision of) the polyhedral complex \(\text{Hom}(K_2,G)\) of graph homomorphisms have the same simple homotopy type, that is, one can be obtained from the other by a finite sequence of collapses and anti-collapses. Here \(K_2\) denotes the complete graph on two nodes.
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Lovaśz complex
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neighborbood complex
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graph complex
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