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- Dmitry N. Kozlov
- Algorithms and computation in mathematics
- 2008

- Dmitry N. Kozlov
- J. Comb. Theory, Ser. A
- 1999

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)

- Dmitry N. Kozlov
- 1999

Let ∆(Πn) denote the order complex of the partition lattice. The natural Sn-action on the set [n] induces an Sn-action on ∆(Πn). We show that the regular CW complex ∆(Πn)/Sn is collapsible. Even more, we show that ∆(Πn)/Sn is collapsible, where Π∆ is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual… (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 colorings. 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 (C2r+1,… (More)

- Dmitry N. Kozlov
- ArXiv
- 2005

We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse

- Dmitry N. Kozlov
- 2009

For positive integers n and d, and the probability function 0 ≤ p(n) ≤ 1, we let Yn,p,d denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d − 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this paper we determine the threshold function for vanishing of the… (More)

- Dmitry N. Kozlov
- 2006

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), whereas… (More)

- Noga Alon, Dmitry N. Kozlov, Van H. Vu
- FOCS
- 1996

Given a set of m coins out of a collection of coins of k unknown distinct weights, we wish to decide if all the m given coins have the same weight or not using the minimum possible number of weighings in a regular balance beam. Let m(n, k) denote the maximum possible number of coins for which the above problem can be solved in n weighings. We show that m(n,… (More)

- Dmitry N. Kozlov
- 2005