In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.

Morton Ann GernsbAcher is the Vilas Research Professor and Sir Frederic C. Bartlett Professor of Psychology at the University of Wisconsin-Madison. She can be reached via email at [email protected]. Around the time I took office as president of the Association for Psychological Science, Wray Herbert, Public Affairs Director of APS, began e-publishing his now syndicated blog,...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The search for a perfect information retrieval (IR) system can be compared to the search for the perfect blended whisky taking inspiration from many components, maturing them together and finally satisfying the needs of a wide range of end-users. Like a blended whisky, IR is currently maturing together components from many constituent research communities, each with their own traditions and cha...

By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the “all-different” constraint. In each of these cases we show that the associated mic...

A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The “strong perfect graph conjecture” (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by C...

abū l-ḥasan alī ibn al-‘abbās al-majūsī ahvazi (? 930-994 ad), best known as haly abbas in the west, was a 10th century persian physician whose lifetime coincided with the flourishing of medical science in the near east, the islamic medicine golden age, an era extending from the 9th to the 12th centuries ad. haly abbas, in his extant book kāmil al-sinā‘ah al-tibbīyah (the perfect book of the ar...