g l o b a l c o m p e t i t i v e n e s s h a s r e c e n t l y b e c o m e a b i g c h a l l e n g e f o r m a n y c o m p a n i e s a r o u n d t h e w o r l d, w h i c h a r e f o r c e d t o s e e k l o w e r c o s t s a n d h i g h e r q u a l i t y f o r w h a t t h e y p r o d u c e. t h e p r o s p e r i t y o f m a n u f a c t u r i n g f i r m s d e p e n d s o n s e l e c t i n g a n...

We prove that every 3-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a set of order Ω ( n log n ) which uses at most two colors, and this bound is tight up to a constant factor. This verifies a conjecture of Hajnal which is a case of the multicolor generalization of the well-known Erdős-Hajnal conjecture. We further establish a generalization of th...

Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r s -fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f , which assigns an s-element subset of the set {1, 2, . . . , r} to each vertex and each edge, moreover, for any color i all vertices of color i induce a subgraph with property P, all edges of color i induce a s...

Obviously, R ⊆ I ⊆ S and thus f (R, k) ≤ f (I, k) ≤ f (S, k) and g(R, k) ≤ g(I, k) ≤ g(S, k) for every k. Note also that f (G, 2) = g(G, 4) for every family G. The results in McGuiness [5] on coloring intersection graphs of arcwise connected sets imply that f (R, k) < ∞ for each integer k. No such facts are known for f (I, k) and f (S, k) and, in fact, the following problems motivated our resea...

An(H , H)-good coloring is the coloring of the edges of a (hyper)graph H such that no subgraph H ⊆ H is monochrome or rainbow. Similarly, we define an (H , H)-proper coloring to be the coloring of the vertices of H with forbidden monochromatic and rainbow copies of H . An (H , Kt)-good coloring is also known as a mixed Ramsey coloring when H = Kn is a complete graph, and an (H , Kt)-proper colo...

in this research, moisture sorptions of sayer date were determined at 20, 30, 40 and 60°c, using the standard static gravimetric method developed by the european cooperation project cost 90. several mathematical models, namely gab, bet, iglesias & chirif and halsey were employed to fit the experimental data through non-linear regression. results indicate that equilibrium moisture content increa...

Let r,k?1 be two integers. An r-hued k-coloring of the vertices a graph G=(V,E) is proper vertices, such that, for every vertex v?V, number colors in its neighborhood at least min{dG(v),r}, where dG(v) degree v. We prove existence an (r+1)-coloring planar graphs with girth 8 r?9. As corollary, maximum ??9 and admits 2-distance (?+1)-coloring.