Skeletal editing involves making specific point-changes to the core of a molecule through selective insertion, deletion or exchange atoms. It thus represents potentially powerful strategy for step-economic modification complex substrates and is perfect complement methods such as C−H functionalization that target molecular periphery. Given their ubiquity in biologically active compounds, ability...

Abstract We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). studied null geodesic equations and obtained BH to see effects PFDM parameter ? , charge Q rotation a it is noticed that size as well shape affected due parameter, parameter. Thus, seen around affects its spacetime. also investigated influence all parameters (PFDM BHs rotati...

We consider the size of circuits that perfectly hash an arbitrary subset S⊂{0, 1} of cardinality 2 into {0, 1}. We observe that, in general, the size of such circuits is exponential in 2k−m, and provide a matching upper bound.

We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.

The amount of at retrieval time is one of the when looking for such functioiis. evidence about the effectivensss reduce the memory requirements perfect hash function proposed

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theory, linear programming and combinatorial optimization. Claude Berge made a conjecture about them, that was proved by Chudnovsky, Robertson, Seymour and Thomas in 2002, and is now called the strong perfect graph theorem. This is a survey about perfect graphs, mostly focused on the strong perfect gr...