### Recent Submissions

• #### Completion and decomposition of hypergraphs into dominating sets of graphs ﻿

(2015-11)
Article
Restricted access - publisher's policy
The collection of the vertex dominating sets of a graph defines a hypergraph on the set of vertices of the graph. However, there are hypergraphs H that are not the collection of the vertex dominating sets of any graph. ...
• #### Geometric biplane graphs II: graph augmentation ﻿

(2015-03-01)
Article
Restricted access - publisher's policy
We study biplane graphs drawn on a finite point set in the plane in general position. This is the family of geometric graphs whose vertex set is and which can be decomposed into two plane graphs. We show that every ...
• #### Geometric biplane graphs I: maximal graphs ﻿

(2015-03-01)
Article
Restricted access - publisher's policy
We study biplane graphs drawn on a finite planar point set in general position. This is the family of geometric graphs whose vertex set is and can be decomposed into two plane graphs. We show that two maximal biplane ...
• #### Empty triangles in good drawings of the complete graph ﻿

(2015)
Article
Restricted access - publisher's policy
A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges ...
• #### A proposal for a workable analysis of Energy Return on Investment (EROI) in agroecosystems. Part I: Analytical approach ﻿

(2015)
Article
Open Access
This paper presents a workable approach to the energy analysis of past and present agroecosystems aimed to contribute to their sustainability assessment. This analysis sees the agroecosystem as a set of energy loops between ...
• #### 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 ...