Articles de revista
http://hdl.handle.net/2117/3197
Wed, 25 Nov 2015 21:17:18 GMT2015-11-25T21:17:18ZEmpty 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.
Thu, 22 Oct 2015 12:57:35 GMThttp://hdl.handle.net/2117/781422015-10-22T12:57:35ZAichholzer, 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.
Tue, 13 Oct 2015 10:29:59 GMThttp://hdl.handle.net/2117/775862015-10-13T10:29:59ZTello, 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.
Wed, 10 Jun 2015 11:51:21 GMThttp://hdl.handle.net/2117/282542015-06-10T11:51:21ZHernando 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)).
Tue, 19 May 2015 11:34:59 GMThttp://hdl.handle.net/2117/279642015-05-19T11:34:59ZFabila 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.
Mon, 13 Apr 2015 10:29:20 GMThttp://hdl.handle.net/2117/272702015-04-13T10:29:20ZFabila-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.
Tue, 24 Mar 2015 10:58:00 GMThttp://hdl.handle.net/2117/269682015-03-24T10:58:00ZGarcia 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.
Wed, 11 Mar 2015 11:14:31 GMThttp://hdl.handle.net/2117/266622015-03-11T11:14:31ZAichholzer, 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.Lower bounds for the number of small convex k-holes
http://hdl.handle.net/2117/26660
Lower bounds for the number of small convex k-holes
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit
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 on h(k)(n), for 3 <= k <= 5. Specifically, we show that h(3)(n) >= n(2) - 32n/7 + 22/7, h(4)(n) >= n(2)/2 - 9n/4 - o(n), and h(5)(n) >= 3n/4 - o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987. (C) 2013 Elsevier B.V. All rights reserved.
Wed, 11 Mar 2015 10:56:59 GMThttp://hdl.handle.net/2117/266602015-03-11T10:56:59ZAichholzer, OswinFabila Monroy, RuyHackl, ThomasHuemer, ClemensPilz, AlexanderVogtenhuber, BirgitLet 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 on h(k)(n), for 3 <= k <= 5. Specifically, we show that h(3)(n) >= n(2) - 32n/7 + 22/7, h(4)(n) >= n(2)/2 - 9n/4 - o(n), and h(5)(n) >= 3n/4 - o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987. (C) 2013 Elsevier B.V. All rights reserved.4-Holes in point sets
http://hdl.handle.net/2117/26659
4-Holes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit
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 minimizing the number of general 4-holes, and maximizing the number of non-convex 4-holes. In particular, we show that for n >= 9, the maximum number of general 4-holes is ((pi)(4)); the minimum number of general 4-holes is at least 5/2 n(2) - circle minus(n); and the maximum number of non-convex 4-holes is at least 1/2 n(3) - circle minus(n(2) logn) and at most 1/2 n(3) - circle minus(n(2)). 2014 (c) Elsevier B.V. All rights reserved.
Wed, 11 Mar 2015 10:45:04 GMThttp://hdl.handle.net/2117/266592015-03-11T10:45:04ZAichholzer, OswinFabila Monroy, RuyGonzalez Aguilar, HernanHackl, ThomasHeredia, Marco A.Huemer, ClemensUrrutia Galicia, JorgeVogtenhuber, BirgitWe 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 minimizing the number of general 4-holes, and maximizing the number of non-convex 4-holes. In particular, we show that for n >= 9, the maximum number of general 4-holes is ((pi)(4)); the minimum number of general 4-holes is at least 5/2 n(2) - circle minus(n); and the maximum number of non-convex 4-holes is at least 1/2 n(3) - circle minus(n(2) logn) and at most 1/2 n(3) - circle minus(n(2)). 2014 (c) Elsevier B.V. All rights reserved.The number of empty four-gons in random point sets
http://hdl.handle.net/2117/26500
The number of empty 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 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 in its interior.
Wed, 25 Feb 2015 11:16:10 GMThttp://hdl.handle.net/2117/265002015-02-25T11:16:10ZFabila-Monroy, RuyHuemer, ClemensMitsche, DieterLet 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 in its interior.