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.

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Dolphins are well known for their complex social and foraging behaviours. Direct underwater observations of wild dolphin feeding behaviour however are rare. At mass spawning aggregations of giant cuttlefish (Sepia apama) in the Upper Spencer Gulf in South Australia, a wild female Indo-Pacific bottlenose dolphin (Tursiops aduncus) was observed and recorded repeatedly catching, killing and prepar...

It is shown that, under mild conditions, a complex reflection group G(r, p, n) may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and a corresponding Hilbert series identity to these and other closely related groups.

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...

A new manganese(II) complex containing p-hydroxybenzoate and caffeine ligands, namely [Mn(OH-C6H4COO)2(H2O)4].2(C8H10N4O2).8H2O has been prepared. The synthesized complex has been characterized by elemental analyses, FT-IR spectroscopy, X-ray crystallography, and m...

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...