We consider the following integer feasibility problem: Given positive integer numbers a0 a1 an, with gcd a1 an = 1 and a = a1 an , does there exist a vector x ∈ n≥0 satisfying a x = a0? We prove that if the coefficients a1 an have a certain decomposable structure, then the Frobenius number associated with a1 an, i.e., the largest value of a0 for which a x= a0 does not have a nonnegative integer...

an h-magic labeling in a h-decomposable graph g is a bijection f : v (g) ∪ e(g) → {1, 2, ..., p + q} such that for every copy h in the decomposition, σνεv(h) f(v) +  σeεe(h) f(e) is constant. f is said to be h-e-super magic if f(e(g)) = {1, 2, · · · , q}. a family of subgraphs h1,h2, · · · ,hh of g is a mixed cycle-decomposition of g if every subgraph hi is isomorphic to some cycle ck, for k ≥ ...

In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.

In the complexity theory of geometric configurations (and other areas of algorithmic endeavor) one encounters a fair number of problems for which a very efficient static solution is known, but no alternative to complete reconstruction seems to come to mind when we wish to insert or delete even a single point. Bentley [1 3 recognized a large class of problems (which he called decomposable search...

Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of this results to Markov chain Monte Carlo methods that sample or optimize over the space of decomposable graphical models according to probabilities determined by a posterior distribution given obser...

Verbal idioms can be divided into two main groups: non-compositional idioms as kick the bucket and composit ional /decomposable idioms as spill the beans. In the following we will point to the fact that there are German decomposable idioms which can be decomposed into components, having identifiable meanings contributing to the meaning of the whole. These idiom compoimnts are taken to have refe...

The junction tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm for building of junction trees sequentially by adding one node at a time to the underlying decomposable graph. The algorithm has two important theoretical properties. Firstly, every junc...