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Combinatorial Algebraic Topology is concerned with computing algebraic invari-ants of combinatorially given cell complexes by combinatorial means. It arises from the quest of explicit descriptions of invariants in Algebraic Topology, and has applications in Discrete Mathematics. In this talk we shall outline the general philosophy of Combinatorial Algebraic(More)
Hom (G, H) is a polyhedral complex defined for any two undirected graphs G and H. This construction was introduced by Lovász to give lower bounds for chromatic numbers of graphs. In this paper we initiate the study of the topological properties of this class of complexes. We show that Hom (K 2 , Kn) is a boundary complex of a polytope, on which the natural(More)
To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to(More)
In this paper we study implications of folds in both parameters of Lovász' Hom(−, −) complexes. There is an important connection between the topological properties of these complexes and lower bounds for chromatic numbers. We give a very short and conceptual proof of the fact that if G − v is a fold of G, then bdHom(G, H) collapses onto bdHom(G − v, H),(More)
For any two graphs G and H Lovász has defined a cell complex Hom (G, H) having in mind the general program that the algebraic invariants of these complexes should provide obstructions to graph col-orings. Here we announce the proof of a conjecture of Lovász concerning these complexes with G a cycle of odd length. More specifically, we show that If Hom(More)
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(More)