27 citations · 70 across the 17 of their papers we have counts for
11 papers · 1 filter
Collapsing along monotone poset maps
Dmitry N. Kozlov
We introduce the notion of nonevasive reduction, and show that for any monotone poset map , the simplicial complex {\tt NE}-reduces to , for any $Q\supseteq{…
Higher connectivity of graph coloring complexes
Sonja Lj. Cukic, Dmitry N. Kozlov
The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom(G,K_n) is at least (n-…
A simple proof for folds on both sides in complexes of graph homomorphisms
Dmitry N. Kozlov
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 complexe…
The homotopy type of complexes of graph homomorphisms between cycles
Sonja Lj. Cukic, Dmitry N. Kozlov
In this paper we study the homotopy type of $\Hom(C_m,C_n)$, where is the cyclic graph with vertices. We enumerate connected components of $\Hom(C_m,C_n)$ and show that e…
Proof of the Lovasz Conjecture
Eric Babson, Dmitry N. Kozlov
To any two graphs G and H one can associate a cell complex Hom(G,H) by taking all graph multihomorphisms from G to H as cells. In this paper we prove the Lovasz Conjecture which st…
Complexes of graph homomorphisms
Eric Babson, Dmitry N. Kozlov
is a polyhedral complex defined for any two undirected graphs and . This construction was introduced by Lovász to give lower bounds for chromatic numbers of graph…