Path parity and perfection

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...

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 ...

Regenerating Perfection.

Path Algorithm for the parity Problem on Linear Patroids

The matroid parity problem is a generalization of rnatroid intersection and general graph matching (and hence network flow, degree-constrained subgraphs, etc.). A polynomial algorithm for linear matroids was presented by L O W l j Z . This paper presents an algorithm that uses time O(nzn3). where m is the number of elements and n is tk,e rank; for the spanning tree parity problem the time ,a O(...

Testing perfection is hard

A graph property P is strongly testable if for every fixed > 0 there is a one-sided -tester for P whose query complexity is bounded by a function of . In classifying the strongly testable graph properties, the first author and Shapira showed that any hereditary graph property (such as P the family of perfect graphs) is strongly testable. A property is easily testable if it is strongly testable ...