Constrained extremal problems for the difference product

Constrained extremal problems in the Hardy space H 2 and

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and uniqueness results, as well as pointwise saturation of the constraint, are established. We also derive a critical point equation which gives rise to a dual formu...

Extremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric

A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...

Extremal Problems for Subset Divisors

Let A be a set of n positive integers. We say that a subset B of A is a divisor of A, if the sum of the elements in B divides the sum of the elements in A. We are interested in the following extremal problem. For each n, what is the maximum number of divisors a set of n positive integers can have? We determine this function exactly for all values of n. Moreover, for each n we characterize all s...

EXTREMAL EIGENVALUE PROBLEMS FOR THE LAPLACIANSteven

Extremal Problems for Roman Domination

A Roman dominating function of a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑ v∈V (G) f(v) over such functions. Let G be a connected n-vertex graph. We prove that γR(G) ≤ 4n/5, and we characterize the graphs achieving equality. We obtain sharp upper and lower bounds for γR(...