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.

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

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.

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...