In this work we study the polytope associated with a 0,1-integer programmingformulation for the Equitable Coloring Problem. We find several families ofvalid inequalities and derive sufficient conditions in order to be facet-defininginequalities. We also present computational evidence that shows the efficacyof these inequalities used in a cutting-plane algorithm.

The article contains analysis of processes and mechanisms for self-fulfillment in professional activities, describes its criteria. It includes results of empiric research of personal determinants behind the individual’s self-fulfillment, broaches the difficulties faced by an individual in his/her self-fulfillment. The work is oriented on the review of personal determinants of the professional s...

For nearly a century (1933 onwards), catalogers and others have engaged in discussions over the 'ethical' labeling of marginalized subjects knowledge organization systems (KOS). In order to understand contextualize contemporary conversations, I undertook comprehensive review this literature. The resulting project 1) synthesizes broader history these discussions, 2) examines its facets subdomain...

An equitable coloring of a graph G is a proper coloring of the vertices of G such that color classes differ in size by at most one. In this note, we verify the equitable coloring conjecture [W. Meyer, Amer. Math. Monthly 80 (1973), 920–922] for some classes of graphs which are defined by forbidden induced subgraphs using known results.

Let H be a k-uniform hypergraph with n vertices. A strong r-coloring is a partition of the vertices into r parts, such that each edge of H intersects each part. A strong r-coloring is called equitable if the size of each part is dn/re or bn/rc. We prove that for all a ≥ 1, if the maximum degree of H satisfies ∆(H) ≤ k then H has an equitable coloring with k a ln k (1 − ok(1)) parts. In particul...

We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. The seminal Hajnal–Szemerédi theorem [12] characterises the minimum degree that ensures a graph G contains a perfect Kr-packing. Balogh, Kostochka and Treglown [4] proposed a degree sequence version of the Hajnal–Szemerédi theorem which, if true, gives a strength...

Freedom of association operates as an organizational “meta-norm,” appreciated both as an independent value and as a touchstone for the institutional design of the International Labour Organization (ILO). Despite the renewed interest of the ILO in various aspects of the norm, its understanding of freedom of association lacks a comprehensive normative framework. This article presents such a conce...

In this note, we consider the permutahedron, the convex hull of all permutations of {1, 2 · · · , n}. We show how to obtain an extended formulation for this polytope from any sorting network. By using the optimal Ajtai-Komlós-Szemerédi (AKS) sorting network, this extended formulation has Θ(n log n) variables and inequalities. Furthermore, from basic polyhedral arguments, we show that this is be...