About perfection of circular mixed hypergraphs

A mixed hypergraph is a triple H = (X,C,D), where X is the vertex set and each of C and D is a family of subsets of X, the C-edges and D-edges, respectively. A proper k-coloring of H is a mapping c : X → {1,...,k} such that each C-edge has two vertices with a common color and each D-edge has two vertices with different colors. Maximum number of colors in a coloring using all the colors is called upper chromatic number χ ̄(H). Maximum cardinality of subset of vertices which contains no C-edge is C-stability number αC (H). A mixed hypergraph is called C-perfect if χ ̄ (H') = αC (H') for any induced subhypergraph H'. A mixed hyper- graph H is called circular if there exists a host cycle on the vertex set X such that every edge (C- or D-) induces a connected subgraph on the host cycle. We give a characterization of C-perfect circular mixed hypergraphs

Transport properties of \nu=1 quantum Hall bilayers. Phenomenological description

We propose a phenomenological model that describes counterflow and drag experiments with quantum Hall bilayers in a \nu_T=1 state. We consider the system consisting of statistically distributed areas with local total filling factors \nu_{T1}>1 and \nu_{T2}<1. The excess or deficit of electrons in a given area results in an appearance of vortex excitations. The vortices in quantum Hall bilayers are charged. They are responsible for a decay of the exciton supercurrent, and, at the same time, contribute to the conductivity directly. The experimental temperature dependence of the counterflow and drive resistivities is described under accounting viscous forces applied to vortices that are the exponentially increase functions of the inverse temperature. The presence of defect areas where the interlayer phase coherence is destroyed completely can result in an essential negative longitudinal drag resistivity as well as in a counterflow Hall resistivity

The Strong Perfect Graph Conjecture: 40 years of Attempts, and its Resolution

International audienceThe Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conjectures in graph theory. During more than four decades, numerous attempts were made to solve it, by combinatorial methods, by linear algebraic methods, or by polyhedral methods. The first of these three approaches yielded the first (and to date only) proof of the SPGC; the other two remain promising to consider in attempting an alternative proof. This paper is an unbalanced survey of the attempts to solve the SPGC; unbalanced, because (1) we devote a signicant part of it to the 'primitive graphs and structural faults' paradigm which led to the Strong Perfect Graph Theorem (SPGT); (2) we briefly present the other "direct" attempts, that is, the ones for which results exist showing one (possible) way to the proof; (3) we ignore entirely the "indirect" approaches whose aim was to get more information about the properties and structure of perfect graphs, without a direct impact on the SPGC. Our aim in this paper is to trace the path that led to the proof of the SPGT as completely as possible. Of course, this implies large overlaps with the recent book on perfect graphs [J.L. Ramirez-Alfonsin and B.A. Reed, eds., Perfect Graphs (Wiley & Sons, 2001).], but it also implies a deeper analysis (with additional results) and another viewpoint on the topic

Credible Equilibria in Games with Utility Changing during the Play

Publicado por Tilburg Center Economic Research 1992Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflicto In this paper we propose an extensiveform game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games