Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs ...

We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable C 5-free graphs diierent from a C 6 and its complement have unique P 4-structure.

inspired by a recent work of buchweitz and flenner, we show that, for a semidualizing bimodule $c$, $c$--perfect complexes have the ability to detect when a ring is strongly regular.it is shown that there exists a class of modules which admit minimal resolutions of $c$--projective modules.

The Wonderful Lemma, that was first proved by Roussel and Rubio, is one of the most important tools in the proof of the Strong Perfect Graph Theorem. Here we give a short proof of this lemma.

Deregulation policy has caused some changes in the concepts of power system reliability assessment. This paper deals with generation reliability evaluation in perfect competition power market using market economic concepts and its dynamic. Also, because of power markets and generators’ forced outages stochastic behavior, Monte Carlo Simulation (MCS) is used in this research. Generation reliabil...

Lagrangian reduction by stages is used to derive the Euler-Poincaré equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous material variables. These order parameters may be regarded geometrically either as objects in a vector space, or as coset spaces of Lie symmetry groups with respe...