In this paper we study a question related to the classical Erdos-Ko-Rado theorem, which states that any family of k-element subsets of the set [n] = {1,..., n} in which any two sets intersect has cardinality at most ((n-1)(k-1)). We say that two non-empty ...
Let d(1) < d(2) < ... denote the set of all distances between two vertices of a convex n-gon. We show that the number of pairs of vertices at distance d(2) from one another is at most n + O(1). (C) 2013 Elsevier B.V. All rights reserved. ...
Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...
We applied first principles molecular dynamics (MD) technique to study structure, dynamics, and magnetic interactions of the Gd3+ aqua ion dissolved in liquid water, a prototypical system for Gd-based complexes used as contrast agents for magnetic res ...