A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ...

Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with |R|=|B| , the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ...

Three polynomials are defined for sets S of n points in general position in the plane: The Voronoi polynomial with coefficients the numbers of vertices of the order-k Voronoi diagrams of S, the circle polynomial with ...

We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ...

Let S be a set of n points in general position in the plane, and let Xk,(S) be the number of convex k-gons with vertices in S that have exactly points of S in their interior. We prove several equalities for the numbers ...

Let S := {p1, . . . , pn} be a set of n points chosen independently and uniformly at random from the unit square and let M be a positive integer. For every point pi = (xi , yi) in S, let p 0 i = (bMxic, bMyic). Let S 0 := ...