Articles de revista
http://hdl.handle.net/2117/3197
2016-02-12T22:31:16ZCompletion and decomposition of hypergraphs into dominating sets of graphs
http://hdl.handle.net/2117/81940
Completion and decomposition of hypergraphs into dominating sets of graphs
Martí Farré, Jaume; Mora Giné, Mercè; Ruiz Muñoz, José Luis
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. This paper deals with the question of completing these hypergraphs H to the vertex dominating sets of some graphs G. We demonstrate that such graphs G exist and, in addition, we prove that these graphs define a poset whose minimal elements provide a decomposition of H. Moreover, we show that the hypergraph H is uniquely determined by the minimal elements of this poset. The computation of such minimal elements is also discussed in some cases.
2016-01-25T09:39:08ZMartí Farré, JaumeMora Giné, MercèRuiz Muñoz, José LuisThe 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. This paper deals with the question of completing these hypergraphs H to the vertex dominating sets of some graphs G. We demonstrate that such graphs G exist and, in addition, we prove that these graphs define a poset whose minimal elements provide a decomposition of H. Moreover, we show that the hypergraph H is uniquely determined by the minimal elements of this poset. The computation of such minimal elements is also discussed in some cases.Geometric biplane graphs II: graph augmentation
http://hdl.handle.net/2117/80900
Geometric biplane graphs II: graph augmentation
Garcia Olaverri, Alfredo Martin; Hurtado, Ferran; Korman Cozzetti, Matias; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D.
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 sufficiently large point set admits a 5-connected biplane graph and that there are arbitrarily large point sets that do not admit any 6-connected biplane graph. Furthermore, we show that every plane graph (other than a wheel or a fan) can be augmented into a 4-connected biplane graph. However, there are arbitrarily large plane graphs that cannot be augmented to a 5-connected biplane graph by adding pairwise noncrossing edges.
2015-12-18T11:39:52ZGarcia Olaverri, Alfredo MartinHurtado, FerranKorman Cozzetti, MatiasMatos, Inés P.Saumell, MariaSilveira, Rodrigo IgnacioTejel Altarriba, Francisco JavierTóth, Csaba D.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 sufficiently large point set admits a 5-connected biplane graph and that there are arbitrarily large point sets that do not admit any 6-connected biplane graph. Furthermore, we show that every plane graph (other than a wheel or a fan) can be augmented into a 4-connected biplane graph. However, there are arbitrarily large plane graphs that cannot be augmented to a 5-connected biplane graph by adding pairwise noncrossing edges.Geometric biplane graphs I: maximal graphs
http://hdl.handle.net/2117/80896
Geometric biplane graphs I: maximal graphs
Garcia Olaverri, Alfredo Martin; Hurtado, Ferran; Korman Cozzetti, Matias; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D.
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 graphs-in the sense that no edge can be added while staying biplane-may differ in the number of edges, and we provide an efficient algorithm for adding edges to a biplane graph to make it maximal. We also study extremal properties of maximal biplane graphs such as the maximum number of edges and the largest maximum connectivity over -element point sets.
2015-12-18T10:43:09ZGarcia Olaverri, Alfredo MartinHurtado, FerranKorman Cozzetti, MatiasMatos, Inés P.Saumell, MariaSilveira, Rodrigo IgnacioTejel Altarriba, Francisco JavierTóth, Csaba D.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 graphs-in the sense that no edge can be added while staying biplane-may differ in the number of edges, and we provide an efficient algorithm for adding edges to a biplane graph to make it maximal. We also study extremal properties of maximal biplane graphs such as the maximum number of edges and the largest maximum connectivity over -element point sets.Empty triangles in good drawings of the complete graph
http://hdl.handle.net/2117/78142
Empty triangles in good drawings of the complete graph
Aichholzer, Oswin; Hackl, Thomas; Pilz, Alexander; Ramos Alonso, Pedro Antonio; Sacristán Adinolfi, Vera; Vogtenhuber, Birgit
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 intersects at most once. In any good drawing, the edges of three pairwise connected vertices form a Jordan curve which we call a triangle. We say that a triangle is empty if one of the two connected components it induces does not contain any of the remaining vertices of the drawing of the graph. We show that the number of empty triangles in any good drawing of the complete graph Kn with n vertices is at least n.
2015-10-22T12:57:35ZAichholzer, OswinHackl, ThomasPilz, AlexanderRamos Alonso, Pedro AntonioSacristán Adinolfi, VeraVogtenhuber, BirgitA 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 intersects at most once. In any good drawing, the edges of three pairwise connected vertices form a Jordan curve which we call a triangle. We say that a triangle is empty if one of the two connected components it induces does not contain any of the remaining vertices of the drawing of the graph. We show that the number of empty triangles in any good drawing of the complete graph Kn with n vertices is at least n.A proposal for a workable analysis of Energy Return on Investment (EROI) in agroecosystems. Part I: Analytical approach
http://hdl.handle.net/2117/77586
A proposal for a workable analysis of Energy Return on Investment (EROI) in agroecosystems. Part I: Analytical approach
Tello, E.; Galán, E.; Cunfer, G.; Guzmán, G.; González de Molina, M.; Krausmann, F.; Gingrich, S.; Sacristán Adinolfi, Vera; Marco, I.; Padró, R.; Moreno-Delgado, D.
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 nature and society, and adopts a farm-operator standpoint at landscape level that involves setting specific system boundaries. This in turn entails a specific form to account for energy outputs as well as inputs. According to this conceptual approach, a clear distinction between Unharvested Phytomass, Land Produce and Final Produce is established, and also a sharp divide is adopted between the energy content of internal flows of Biomass Reused and external Societal Inputs when accounting for the amount of Total Inputs Consumed . Treating the conversion of solar radiation into local biomass as a gift of nature, enthalpy values of energy carriers are accounted for net Final Produce going outside as well as for Biomass Reused or Unharvested Phytomass , given that all these flows are evaluated from inside the agroecosystem. On the other hand, the external energy carriers are accounted for as embodied values by adding up direct and indirect energy carriers required to produce or deliver these Societal Inputs to the agroecosystem. The human Labour performed by the farm operators is treated as a special case of external input. It is accounted for the fraction of their energy intake devoted to perform agricultural work, by only using enthalpy or adding transport embodied values depending on the local or external origin of ingredients of the food basket. Following this line of reasoning we propose the definition of two different sets of agroecosystem’s Energy Returns On Energy Inputs (EROIs), depending on whether we use as numerator the Final Produce or the total phytomass harvested and unharvested included in the actual Net Primary Production. By comparing Final EROI with NPP act EROI we can obtain a proxy useful to assess whether the different paths taken by the energy throughputs may undermine or not biodiversity and soil fertility in agroecosystems. Then, by alternatively including or excluding Biomass Reused and External Inputs in the denominator, we split Final EROI into their respective energy returns to either internal or external inputs. This leads to a four interrelated EROIs whose meanings, shortcomings or ambiguities are examined respectively, in order to combine them all to draw the sociometabolic energy profiles of different sorts of agroecosystems along the socio-ecological transitions from traditional organic to industrial farm systems. The conceptual and quantitative relationships between the internal and external returns of Final EROI provide a method to decompose both dimensions in a way that clarifies their respective roles when comparing different agroecosystems, and reveals their capacity for increasing energy yields. This decomposition analysis also facilitates graphing their changing energy profiles through socio-ecological transitions along history. Finally, we suggest other related or derived indicators that can be useful for different purposes. With the bookkeeping proposed the energy analysis of farm systems is widened so as to highlight the role played by the biomass unharvested or internally reused in keeping the ecological services that biodiversity and soil fertility provide. This may also allow to test in agro-forest mosaics the Intermediate Disturbance Hypothesis long debated in ecology, by linking our energy analysis with landscape ecology metrics.
2015-10-13T10:29:59ZTello, E.Galán, E.Cunfer, G.Guzmán, G.González de Molina, M.Krausmann, F.Gingrich, S.Sacristán Adinolfi, VeraMarco, I.Padró, R.Moreno-Delgado, D.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 nature and society, and adopts a farm-operator standpoint at landscape level that involves setting specific system boundaries. This in turn entails a specific form to account for energy outputs as well as inputs. According to this conceptual approach, a clear distinction between Unharvested Phytomass, Land Produce and Final Produce is established, and also a sharp divide is adopted between the energy content of internal flows of Biomass Reused and external Societal Inputs when accounting for the amount of Total Inputs Consumed . Treating the conversion of solar radiation into local biomass as a gift of nature, enthalpy values of energy carriers are accounted for net Final Produce going outside as well as for Biomass Reused or Unharvested Phytomass , given that all these flows are evaluated from inside the agroecosystem. On the other hand, the external energy carriers are accounted for as embodied values by adding up direct and indirect energy carriers required to produce or deliver these Societal Inputs to the agroecosystem. The human Labour performed by the farm operators is treated as a special case of external input. It is accounted for the fraction of their energy intake devoted to perform agricultural work, by only using enthalpy or adding transport embodied values depending on the local or external origin of ingredients of the food basket. Following this line of reasoning we propose the definition of two different sets of agroecosystem’s Energy Returns On Energy Inputs (EROIs), depending on whether we use as numerator the Final Produce or the total phytomass harvested and unharvested included in the actual Net Primary Production. By comparing Final EROI with NPP act EROI we can obtain a proxy useful to assess whether the different paths taken by the energy throughputs may undermine or not biodiversity and soil fertility in agroecosystems. Then, by alternatively including or excluding Biomass Reused and External Inputs in the denominator, we split Final EROI into their respective energy returns to either internal or external inputs. This leads to a four interrelated EROIs whose meanings, shortcomings or ambiguities are examined respectively, in order to combine them all to draw the sociometabolic energy profiles of different sorts of agroecosystems along the socio-ecological transitions from traditional organic to industrial farm systems. The conceptual and quantitative relationships between the internal and external returns of Final EROI provide a method to decompose both dimensions in a way that clarifies their respective roles when comparing different agroecosystems, and reveals their capacity for increasing energy yields. This decomposition analysis also facilitates graphing their changing energy profiles through socio-ecological transitions along history. Finally, we suggest other related or derived indicators that can be useful for different purposes. With the bookkeeping proposed the energy analysis of farm systems is widened so as to highlight the role played by the biomass unharvested or internally reused in keeping the ecological services that biodiversity and soil fertility provide. This may also allow to test in agro-forest mosaics the Intermediate Disturbance Hypothesis long debated in ecology, by linking our energy analysis with landscape ecology metrics.On global location-domination in graphs
http://hdl.handle.net/2117/28254
On global location-domination in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
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 are called LD-codes and the cardinality of an LD-code is the location-domination number lambda(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complement G'. The global location-domination number lambda g(G) is introduced as the minimum cardinality of a global LD-set of G.
In this paper, some general relations between LD-codes and the location-domination number in a graph and its complement are presented first.
Next, a number of basic properties involving the global location-domination number are showed. Finally, both parameters are studied in-depth for the family of block-cactus graphs.
2015-06-10T11:51:21ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA 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 are called LD-codes and the cardinality of an LD-code is the location-domination number lambda(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complement G'. The global location-domination number lambda g(G) is introduced as the minimum cardinality of a global LD-set of G.
In this paper, some general relations between LD-codes and the location-domination number in a graph and its complement are presented first.
Next, a number of basic properties involving the global location-domination number are showed. Finally, both parameters are studied in-depth for the family of block-cactus graphs.Empty non-convex and convex four-gons in random point sets
http://hdl.handle.net/2117/27964
Empty non-convex and convex four-gons in random point sets
Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter
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 non-convex four-gons with vertices from S is 12 n(2) log n + o(n(2) log n) and the expected number of empty convex four-gons with vertices from S is Theta(n(2)).
2015-05-19T11:34:59ZFabila Monroy, RuyHuemer, ClemensMitsche, DieterLet 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 non-convex four-gons with vertices from S is 12 n(2) log n + o(n(2) log n) and the expected number of empty convex four-gons with vertices from S is Theta(n(2)).Note on the number of obtuse angles in point sets
http://hdl.handle.net/2117/27270
Note on the number of obtuse angles in point sets
Fabila-Monroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia
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 to show the upper bound $\frac{2n^3}{27}-O(n^2)$ on the minimum number of obtuse angles among all sets $S$.
We prove that every set $S$ of $n$ points in convex position determines at least $\frac{2n^3}{27}-o(n^3)$ obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case.
Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved.
2015-04-13T10:29:20ZFabila-Monroy, RuyHuemer, ClemensTramuns, EulàliaIn $1979$ 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 to show the upper bound $\frac{2n^3}{27}-O(n^2)$ on the minimum number of obtuse angles among all sets $S$.
We prove that every set $S$ of $n$ points in convex position determines at least $\frac{2n^3}{27}-o(n^3)$ obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case.
Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved.Compatible spanning trees
http://hdl.handle.net/2117/26968
Compatible spanning trees
Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier
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 of S. In this work, we study the problem of finding a second plane geometric tree T' spanning S, such that is compatible with T and shares the minimum number of edges with T. We prove that there is always a compatible plane geometric tree T' having at most #n - 3#/4 edges in common with T, and that for some plane geometric trees T, any plane tree T' spanning S, compatible with T, has at least #n - 2#/5 edges in common with T. #C# 2013 Elsevier B.V. All rights reserved.
2015-03-24T10:58:00ZGarcia Olaverri, Alfredo MartinHuemer, ClemensHurtado Díaz, Fernando AlfredoTejel Altarriba, Francisco JavierTwo 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 of S. In this work, we study the problem of finding a second plane geometric tree T' spanning S, such that is compatible with T and shares the minimum number of edges with T. We prove that there is always a compatible plane geometric tree T' having at most #n - 3#/4 edges in common with T, and that for some plane geometric trees T, any plane tree T' spanning S, compatible with T, has at least #n - 2#/5 edges in common with T. #C# 2013 Elsevier B.V. All rights reserved.Empty monochromatic simplices
http://hdl.handle.net/2117/26662
Empty monochromatic simplices
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge
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 d-simplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3a parts per thousand currency signka parts per thousand currency signd we provide a lower bound of and strengthen this to Omega(n (d-2/3)) for k=2.; On the way we provide various results on triangulations of point sets in . In particular, for any constant dimension da parts per thousand yen3, we prove that every set of n points (n sufficiently large), in general position in , admits a triangulation with at least dn+Omega(logn) simplices.
2015-03-11T11:14:31ZAichholzer, OswinFabila Monroy, RuyHackl, ThomasHuemer, ClemensUrrutia Galicia, JorgeLet 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 d-simplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3a parts per thousand currency signka parts per thousand currency signd we provide a lower bound of and strengthen this to Omega(n (d-2/3)) for k=2.; On the way we provide various results on triangulations of point sets in . In particular, for any constant dimension da parts per thousand yen3, we prove that every set of n points (n sufficiently large), in general position in , admits a triangulation with at least dn+Omega(logn) simplices.