A graph is Berge if no induced subgraph of it is an odd cycle of length at least five or the complement of one. In joint work with Robertson, Seymour, and Thomas we recently proved the Strong Perfect Graph Theorem, which was a conjecture about the chromatic number of Berge graphs. The proof consisted of showing that every Berge graph either belongs to one of a few basic classes, or admits one o...

A rigidly rotating incompressible perfect fluid solution of Einstein’s gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the instantaneous constantpressure surfaces is positive and they have two ring-shaped cusps. PACS numbers: 04.20.Cv, 04.20.Jb, 04.40.Dg, 97.60.-s Rotating perfect fluid solutions of the...

We prove that if $R$ is a commutative Noetherian ring, then every countably generated flat $R$-module quite flat, i.e., direct summand of transfinite extension localizations in countable multiplicative subsets. also show the spectrum cardinality less than $\kappa$, where $\kappa$ an uncountable regular cardinal, modules with generators. This provides alternative proof fact over ring spectrum, a...

Perfect simulation of an one-dimensional loss network on R with length distribution π and cable capacity C is performed using the clan of ancestors method. Domination of the clan of ancestors by a branching process with longer memory improves the sufficient conditions for the perfect scheme to be applicable.

Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover Q and a stable set cover S s.t. every clique in Q intersects every stable set in S. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (K ̈orner [6]) and graph entropy (Czisz ́ar et al. [5]). Perfect graphs have been recently characterized a...

CCC-r chart extended approach of CCC charts, is a technique applied when nonconforming items are rarely observed. However, it is usually assumed that the inspection process is perfect in the implementation control charts imperfect inspections may have a significant impact on the performance of the control chart and setting the control limits. This paper first investigates the ...

The existence of small d-regular graphs of a prescribed girth g is equivalent to the existence of certain codes in the d-regular infinite tree. We show that in the tree ‘‘perfect’’ codes exist, but those are usually not ‘‘graphic’’. We also give an explicit coloring that is ‘‘nearly perfect’’ as well as ‘‘nearly graphic’’. r 2004 Elsevier Inc. All rights reserved.