"... Reiner proposed two conjectures about the structure of the critical group of the n-cube Qn. In this paper we confirm them. Furthermore we describe its p-primary structure for all odd primes p. The results are generalized to Cartesian product of complete graphs Kn1 ×···× Knk by Jacobson, Niedermaier ..."
"... For a given connected graph G of order n, a routing R is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passingthrough any vertex (resp. edge) in the graph. In this paper, t ..."
"... Abstract. A path bundle is a set of 2 a paths in an n-cube, denoted Qn, such that every path has the same length, the paths partition the vertices of Qn, the endpoints of the paths induce two subcubes of Qn, and the endpoints of each path are complements. This paper shows that a path bundle exists i ..."
"... Let C " denote the graph with vertices @I,. . . ,e,,) , ei = 0,i and vertices adjacent if they differ in exactly one coordinate. We call C " the n-cube. Let G = G., denote the random subgraph of C " defined by letting Prob(IijlEG)=p for ah & jE CR and letting these probabilities be mutually ..."
"... We study the skeleton of several polytopes related to the n-cube, the halved n-cube, and the folded n-cube. In particular, the Gale polytope of the n-cube, its dual and the duals of the halved n-cube and the complete bipartite subgraphs polytope. 1 Introduction The general references are [?, ?, ..."
"... . Let an edge cut partition the vertex set of the n-cube into k subsets A1 ; :::; Ak with jjA i j \Gamma jA j jj 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n; k !1 and also as n !1 and k is a constant of the form k = 2 a \Sigma 2 b with a ..."
"... We define an interconnection network AQn,k which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQn,k has a number of attractive ..."
"... In this paper we show that if a cosimplicial space has a certain kind of combinatorial structure then its total space has an action of an operad weakly equivalent to the little n-cubes operad. Our results are also valid for cosimplicial spectra. 1 Introduction. The little n-cubes operad Cn was intro ..."