Homotopy types of the Hom complexes of graphs
نویسندگان
چکیده
منابع مشابه
Homotopy groups of Hom complexes of graphs
The notion of ×-homotopy from [Doca] is investigated in the context of the category of pointed graphs. The main result is a long exact sequence that relates the higher homotopy groups of the space Hom∗(G,H) with the homotopy groups of Hom∗(G,H ). Here Hom∗(G,H) is a space which parameterizes pointed graph maps from G to H (a pointed version of the usual Hom complex), and H is the graph of based...
متن کاملHom complexes and homotopy in the category of graphs
We investigate a notion of ×-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph ×homotopy is characterized by the topological properties of the Hom complex, a functorial way to assign a poset (and hence topological space) to a pair of graphs; Hom complexes were introduced by Lovász and further studied ...
متن کاملHom complexes and homotopy theory in the category of graphs
We investigate a notion of ×-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph ×homotopy is characterized by the topological properties of the Hom complex, a functorial way to assign a poset (and hence topological space) to a pair of graphs; Hom complexes were introduced by Lovász and further studied ...
متن کاملSimple Homotopy Types of Hom-complexes, Neighborhood Complexes, Lovász Complexes, and Atom Crosscut Complexes
In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...
متن کاملThe universality of Hom complexes of graphs
It is shown that given a connected graph T with at least one edge and an arbitrary finite simplicial complex X, there is a graph G such that the complex Hom(T,G) is homotopy equivalent to X. The proof is constructive, and uses a nerve lemma. Along the way several results regarding Hom complexes, exponentials of graphs, and subdivisions are established that may be of independent interest.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2017
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2017.03.009