# Sergei L. Bezrukov

We consider subsets of the n-dimensional grid with the Manhattan metrics, (i.e. the Cartesian product of chains of lengths k1, . . . , kn) and study those of them which have maximal number of induced edges of the grid, and those which are separable from their complement by the least number of edges. The first problem was considered for k1 = · · · = kn by(More)
• Discrete Mathematics
• 2000
We consider the problem of embedding the n-dimensional cube into a rectangular grid with 2n vertices in such a way as to minimize the congestion, the maximum number of edges along any point of the grid. After presenting a short solution for the cutwidth problem of the n-cube (in which the n-cube is embedded into a path), we show how to extend the results to(More)
We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for such embeddings, namely the sum over i = 1, ..., n of dilations and the sum of edge(More)
Let g,h be partial mappings of {1, 2, ..., n} into {0, 1, ..., k} and D(g),D(h) be their domains. We say that h is greater or equal to g iff D(h) ⊆ D(g) and g(x) = h(x) for all x ∈ D(h). The collection of all partial mappings with the order just defined forms the ranked poset, which we denote by F n k . We may assign to each mapping g a vector ã = (a1, ...,(More)
We present here constructions of ideals A of the poset of n-vectors (x1, ..., xn) with integer entries, ordered coordinatewise, on which the maximal and minimal values of Wφ(A) = ∑ x∈A φ( ∑n i=1 xi) are achieved for a given unimodal function φ. As a consequence we get a new approach to prove the well-known ClementsLindström Theorem [6].
In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph Pn, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of Pn are also derived. These results are then generalized for the cartesian product of(More)
• Combinatorics and Computer Science
• 1995
We consider the collection of all spanning trees of a graph with distance between them based on the size of the symmetric difference of their edge sets. A central spanning tree of a graph is one for which the maximal distance to all other spanning trees is minimal. We prove that the problem of constructing a central spanning tree is algorithmically(More)
• Discrete Applied Mathematics
• 1998
We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the embeddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.