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...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...

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.

Let G be a connected graph that is the edge-disjoint union of two paths of length n, where n ≥ 2. Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that G has a third path of length n. The “two-path conjecture” states that if a graph G is the edge-disjoint union of two paths of length n with at least one common vertex, then the graph has...