It is known that in case the distance matrix in the Travelling Salesman Problem (TSP) fulllls certain combinatorial conditions (e.g. the Demidenko conditions , the Kalmanson conditions or the Supnick conditions) then the TSP is solvable in polynomial time. This paper deals with the problem of recognizing Euclidean instances of the TSP for which there is a renumbering of the cities such that the...

The development of multicomponent reactions (MCRs) designed to produce elaborate biologically active compounds has become an important area of research in organic, combinatorial, and medicinal chemistry. A comparative study of the synthesis of new bis-spiro-oxindolo(pyrrolizidines/pyrrolidines) ring systems by the cycloaddition of azomethine ylides generated by a decarboxylative route from sarc...

Multi-component epitaxial thin films have been studied extensively to produce new functional materials, such as superconductors and optical and magnetic devices. In order to optimize the material properties and obtain high-performance devices, we need to determine a large number of parameters, for example, the composition, structure of layers, superlattice periods and so on. Combinatorial synth...

Experimental design focuses on describing or explaining the multifactorial interactions that are hypothesized to reflect the variation. The design introduces conditions that may directly affect the variation, where particular conditions are purposely selected for observation. Combinatorial design theory deals with the existence, construction and properties of systems of finite sets whose arrang...

We consider the following conjecture proposed by Cornuéjols, Guenin and Margot: every ideal minimally non-packing clutter has a transversal of size 2. For a clutter C, let C̃ denote the set of hyperedges of C which intersect any minimum transversal in exactly one element. We divide the (non-)existence problem of an ideal minimally non-packing clutter D into two steps. In the first step, we give ...