Provan and Billera defined the notion of weak k-decomposability for pure simplicial complexes in the hopes of bounding the diameter of convex polytopes. They showed the diameter of a weakly k-decomposable simplicial complex ã is bounded above by a polynomial function of the number of k-faces in ã and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of verti...

Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...

We investigate under what conditions a co-recursively enumerable set S in a computable metric space (X, d, α) is recursive. The topological properties of S play an important role in view of this task. We first study some properties of computable metric spaces such as the effective covering property. Then we examine co-r.e. sets with disconnected complement, and finally we focus on study of chai...

Given a tournament T, module of T is subset M V(T) such that for $$x, y\in M$$ and $$v\in V(T)\setminus , $$(v,x)\in A(T)$$ if only $$(v,y)\in . The trivial modules are $$\varnothing$$ $$\{u\}$$ $$(u\in V(T))$$ V(T). indecomposable all its trivial; otherwise it decomposable. Let be with at least five vertices. In previous paper, the authors proved smallest number $$\delta (T)$$ arcs must revers...

Let G be a graph of order n and r , 1 ≤ r ≤ n, a fixed integer. G is said to be r -vertex decomposable if for each sequence (n1, . . . , nr ) of positive integers such that n1 + · · · + nr = n there exists a partition (V1, . . . , Vr ) of the vertex set of G such that for each i ∈ {1, . . . , r}, Vi induces a connected subgraph of G on ni vertices. G is called arbitrarily vertex decomposable if...

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...

Let X be a finite set of cardinality n. The Kalmanson complex Kn is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine Kn from three perspectives. In addition to the T -theoretic description, we show that Kn has a geometric realization as the Kalmanson conditions on a finite metric. A third descrip...

Even the most super cial glance at the vast majority of crossing-minimal geometric drawings of Kn reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply 3-symmetric). And second, they all are 3-decomposable, that is, there is a triangle T enclosing the drawing, and a balanced partition A,B, C of the underlying set of points P , such that the orthogo...

This paper studies the impact of task complexity and decomposability on the degree of organizational divisionalization and hierarchy within firms. Drawing upon the team theory and modularity literature, it argues that the degree of divisionalization is predicated not only on the extent of interdependence (complexity) among tasks but also on the extent to which those interdependent relationships...

The permutahedron Perm(P) of a poset P is defined as the convex hull of those permutations that are linear extensions of P. Von Arnim et al. (1990) gave a linear description of the permutahedron of a series-parallel poset. Unfortunately, their main theorem characterizing the facet defining inequalities is only correct for not series-decomposable posets. We do not only give a proof of the revise...