### Recent Submissions

• #### On global location-domination in graphs ﻿

(2015-05-29)
Article
Open Access
A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality ...
• #### Empty non-convex and convex four-gons in random point sets ﻿

(2015-03-01)
Article
Open Access
Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty ...
• #### Note on the number of obtuse angles in point sets ﻿

(2014-09)
Article
Open Access
In $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}-O(n^2)$ obtuse angles and also presented a special set of $n$ points ...
• #### Compatible spanning trees ﻿

(2014-07-01)
Article
Open Access
Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ...
• #### Lower bounds for the number of small convex k-holes ﻿

(2014-07-01)
Article
Open Access
Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ...
• #### 4-Holes in point sets ﻿

(2014-08-01)
Article
Open Access
We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...
• #### Empty monochromatic simplices ﻿

(2014-03-01)
Article
Open Access
Let S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...
• #### The number of empty four-gons in random point sets ﻿

(2014)
Article
Open Access
Let S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty four-gons with vertices from S is T(n^2 log¿ n). A four-gon is empty if it contains no points of S ...
• #### Witness rectangle graphs ﻿

(2014-07)
Article
Restricted access - publisher's policy
In a witness rectangle graph (WRG) on vertex point set P with respect to witness point set W in the plane, two points x, y in P are adjacent whenever the open isothetic rectangle with x and y as opposite corners contains ...
• #### The degree/diameter problem in maximal planar bipartite graphs ﻿

(2014)
Article
Open Access
The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, ...