Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.

We continue a recent systematic study into the clique-width of (H1, H2)-free graphs and present five new classes of (H1, H2)-free graphs of bounded clique-width. As a consequence, we have reduced the number of open cases from 13 to 8. Four of the five new graph classes have in common that one of their two forbidden induced subgraphs is the triangle. As such, we generalize corresponding results ...

Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G ? v with the additional edge-set fxy : x 2 V (H); y 2 N G (v)g. For a hereditary class of graphs P, the substitutional closure of P is deened as the class P consisting of all graphs which can be obtained from graphs in P by repeated substitutions. Let ...

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.

In this work, mechanical alloying was employed to produce Ti-50Al and Ti-45Al-5Cr (at%) alloys. Alloying was performed in a planetary mill and the alloying time varying from 5 to 70h. Characterization of the powder mixture was performed by X-ray diffraction (XRD), SEM analyses and DTA test, during mechanical alloying and after annealing at 1100°c in vacuum oven. The results showed, after 50h of...

Liquid-liquid equilibrium (LLE) problems such as phase stability analysis, phase equilibrium calculations, chemical equilibrium calculations, binary interaction parameter identification of thermodynamic models and other problems of fluid characterization have been the core subject of many recent studies. This study introduces Cuckoo Search (CS), Firefly Algorithms (FA) and its variants as p...