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.

This paper presents “oriented pivoting systems” as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash equilibria of a bimatrix game at the ends of Lemke–Howson paths, which have opposite index. For Euler complexes or “oiks”, an orientation is defined which extends th...

Perfectionists have excessively high standards and thus are prone to experience dissatisfaction and embarrassment. But what if they achieve perfection? The present study investigated in a sample of 194 university students how self-oriented and socially prescribed perfectionism predicted emotional reactions (satisfaction, dissatisfaction, pride, embarrassment) to imagined situations in which stu...

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.

In this paper, a new letter-oriented perfect hashing scheme based on Ziegler’s row displacement method is presented. A unique n -tuple from a given set of static letter-oriented key words can be extracted by a heuristic algorithm. Then the extracted distinct n -tuples are associated with a 0/1 sparse matrix. Using a sparse matrix compression technique, a perfect hashing function on the key word...

A hierarchical framework is proposed to address the issues of modeling different type of words in keyword spotting (KWS). Keyword models are built at various levels according to the availability of training set resources for each individual word. The proposed approach improves the performance of KWS even when no training speech is available for the keywords. It also suggests an easier way to co...