Factorization of measures and perfection

Profiling, Performance, and Perfection

A profile is “a set of data often in graphic form portraying the significant features of something”. [Web88] Profiles can help us to quickly understand a person or entity better. In the development of computer-based applications, profiles are invaluable. They help us to understand the application – how it works, how well it works, whether it in fact works as we think it does, and whether it is ...

Path parity and perfection

Two non-adjacent vertices x and y in a graph G form an even pair if every induced path between them has an even number of edges. For a given pair fx; yg in a graph G, we denote by G xy the graph obtained from G by contracting x and y. In 1982, Fonlupt and Uhry proved that if G is perfect then so is G xy. In 1987, Meyniel used this fact to prove that no minimal imperfect graph contains an even p...

Perfection thickness of graphs

We determine the order of growth of the worst-case number of perfect subgraphs needed to cover an n-vertex graph.

Regenerating Perfection.

On the WZ Factorization of the Real and Integer Matrices

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...