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...

A Roman dominating function (RD-function) on a graph G = ( V , E ) is f : → {0, 1, 2} satisfying the condition that every vertex u for which 0 adjacent to at least one v 2. An in perfect (PRD-function) if with exactly The (perfect) domination number γ R p )) minimum weight of an . We say strongly equals ), denoted by ≡ γR RD-function PRD-function. In this paper we show given it NP-hard decide w...

Introduction: Arginine-phenylalanine-amide-related peptide-3 (RFRP-3) is an inhibitor of gonadotropin releasing hormone (GnRH) secretion and an appetizer. Kisspeptin is a stimulator of GnRH and a regulator of energy metabolism. The objectives of the present study were to compare the effect of long term malnutrition on expression of RFRP-3 mRNA in dorsomedial hypothalamic nucleus (DMH) and Ki...

Hoang, C.T., F. Maffray, S. Olariu and M. Preissmann, A charming class of perfectly orderable graphs, Discrete Mathematics 102 (1992) 67-74. We investigate the following conjecture of VaSek Chvatal: any weakly triangulated graph containing no induced path on five vertices is perfectly orderable. In the process we define a new polynomially recognizable class of perfectly orderable graphs called ...

1. Let F be a partially ordered vector space with an order unit e. It is well known that the class 5DÎ of maximal ideals of V is in one-one correspondence with the class K of normalized positive linear functionals, in the sense that to each ME^SR corresponds a positive linear functional <¡>m with M as its null-space and with M(e) = 1. A maximal ideal MG 90? is said to be extreme if <pM is an...

Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.

A 2-matching in an undirected graph G = (V G,EG) is a function x : EG → {0, 1, 2} such that for each node v ∈ V G the sum of values x(e) on all edges e incident to v does not exceed 2. The size of x is the sum ∑ e x(e). If {e ∈ EG | x(e) 6= 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial O(mn)-algorithm that finds a triangle free 2-mat...

A c-ary Perfect Factor is a set of uniformly long cycles whose elements are drawn from a set of size c, in which every possible v-tuple of elements occurs exactly once. In the binary case, i.e. where c = 2, these perfect factors have previously been studied by Etzion, [2], who showed that the obvious necessary conditions for their existence are in fact sufficient. This result has recently been ...