Dissections, Hom-complexes and the Cayley trick
We show that certain canonical realizations of the complexes $\Hom(G,H)$ and $\Hom_+(G,H)$ of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For $G$~a complete graph, we then characterize when a canonical projection of these complexes...
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| Formato: | artículo |
| Fecha de publicación: | 2006 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/433 |
| Acesso em linha: | https://hdl.handle.net/2117/433 |
| Access Level: | acceso abierto |
| Palavra-chave: | Discrete geometry Polytopes Cayley trick Polygon dissection polytopal complex clique number Geometria combinatòria Geometria discreta Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta |
| Resumo: | We show that certain canonical realizations of the complexes $\Hom(G,H)$ and $\Hom_+(G,H)$ of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For $G$~a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of such projected $\Hom$-complexes: the dissections of a convex polygon into $k$-gons, Postnikov's generalized permutohedra, staircase triangulations, the complex dual to the lower faces of a cyclic polytope, and the graph of weak compositions of an integer into a fixed number of summands. |
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