We show that recursive circulant G(cd m ; d) is hamiltonian decomposable. Recursive circulant is a graph proposed for an interconnection structure of multicomputer networks in [8]. The result is not only a partial answer to the problem posed by Alspach that every connected Cayley graph over an abelian group is hamiltonian decomposable, but also an extension of Micheneau's that recursive circula...

In this paper, we study the problem of decomposing a given tensor into train such that tensors at vertices are orthogonally decomposable. When has length two, and decomposable two symmetric, recover decomposition by considering random linear combinations slices. Furthermore, if symmetric low-rank but not decomposable, show whitening procedure can transform orthogonal case. network three or more...

We introduce the notion of an Eulerian graph being strongly evencycle decomposable, and note that a few basic classes have this property. Our main results are that several fundamental composition operations that preserve the property of being Eulerian also preserve the property of being strongly even-cycle decomposable. As an application, our composition operations easily imply that all Euleria...

We use Shelah’s theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem 1. Suppose that λ is a singular cardinal, λ′ < λ, and the ultrafilter D is κ-decomposable for all regular cardinals κ with λ′ < κ < λ. Then D is either λ-decomposable, or λ-decomposable. Corollary 2. If λ is a singular cardinal, then an ultrafilter is (λ, λ)-regular if and only if it is e...

We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin–Courant, as the only rules in certain in...

In this paper, we investigate the interactions between Legendrian satellite construction and existence of exact, orientable Lagrangian cobordisms knots. Given two knots tangles, construct a cobordism satellites by closures with extra twists on both top bottom to compensate for genus cobordism. If original were decomposable, then decomposable exists as well, again twists.

We consider the calculation of quantum mechanical rate constants for chemical reactions via algorithms that utilize short-time values of the symmetrized flux-flux correlation function. We argue that the dividing surface that makes optimal use of the short-time quantum information is the surface that minimizes the value at the origin of the symmetrized flux-flux correlation function. We also dem...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal dist...