In this paper, we address a particular variation of the Turán problem for the hypercube. Alon, Krech and Szabó (2007) asked “In an n-dimensional hypercube, Qn, and for ` < d < n, what is the size of a smallest set, S, of Q`’s so that every Qd contains at least one member of S?” Likewise, they asked a similar Ramsey type question: “What is the largest number of colors that we can use to color th...

We describe a general framework for covering concepts using terminologies and briefly present the already investigated instances of this framework. Then, we formalize the best covering problem in the context of the ALN language, in which the difference operation is not semantically unique, and sketches the technique to solve the underlying computation problems.

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds (Kähler groups) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.

in this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. we also consider flexibility on distance standard for covering demand nodes by the servers. we use the satisfaction degree to represent the constraint of service capacity. the proposed model belongs to the class of mixed integer programming models. our model can be redu...

We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.