The recently announced Strong Perfect Graph Theorem states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two b...

The theory of perfect graphs relates the concept of graph colorings to the concept of cliques. In this paper, we introduce the concept of a perfect graph as well as a number of graph classes that are always perfect. We next introduce both theWeak Perfect Graph Theorem and the Strong Perfect Graph Theorem and provide a proof of the Weak Perfect Graph Theorem. We also demonstrate an application o...

We study the problem of encoding cardinality constraints (threshold functions) on Boolean variables into CNF. Specifically, we propose new encodings based on (perfect) hashing that are efficient in terms of the number of clauses, auxiliary variables, and propagation strength. We compare the properties of our encodings to known ones, and provide experimental results evaluating their practical ef...

This essay examines the use of famine-plot rhetoric in the course of disputes over free trade in the French Atlantic during the late eighteenth century. Seeking to discredit officially sanctioned trade monopolies, French plantation owners frequently suggested that the control exercised by metropolitan merchants over transatlantic commerce was responsible for food shortages among the enslaved po...

Results of Lovász and Padberg entail that the class of so-called partitionable graphs contains all the potential counterexamples to Berge’s famous Strong Perfect Graph Conjecture, which asserts that the only minimal imperfect graphs are the odd chordless cycles with at least five vertices (”odd holes”) and their complements (”odd antiholes”). Only two constructions (due to Chvátal, Graham, Pero...

The Strong Perfect Graph Conjecture, suggested by Claude Berge in 1960, had a major impact on the development of graph theory over the last forty years. It has led to the definitions and study of many new classes of graphs for which the Strong Perfect Graph Conjecture has been verified. Powerful concepts and methods have been developed to prove the Strong Perfect Graph Conjecture for these spec...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...