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      On 4-connected geometric graphs 

      García Olaverri, Alfredo; Huemer, Clemens; Tejel Altarriba, Francisco Javier; Valtr, Pavel (2013)
      Given a set S of n points in the plane, in this paper we give a necessary and sometimes sufficient condition to build a 4-connected non-crossing geometric graph on S.
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      Abstract Voronoi diagrams 

      Klein, Rolf (2013)
      Abstract Voronoi diagrams are a unifying framework that covers many types of concrete Voronoi diagrams. This talk reports on the state of the art, including recent progress.
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      A symbolic-numeric dynamic geometry environment for the computation of equidistant curves 

      Abánades Astudillo, Miguel Ángel; Botana Ferreiro, Francisco (2013)
      A web-based system that determines point/curve and curve/curve bisectors in a dynamic geometry system in a completely ...
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      On the nonexistence of k-reptile simplices in R3 and R4 

      Kynčl, Jan; Safernova, Zuzana (2013)
      A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled without overlaps by k simplices ...
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      Drawing the double circle on a grid of minimum size 

      Bereg, Sergey; Fabila Monroy, Ruy; Flores Peñaloza, David; Lopez, Mario A.; Pérez Lantero, Pablo (2013)
      In 1926, Jarník introduced the problem of drawing a convex n-gon with vertices having integer coordinates. He constructed ...
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      Note on the number of obtuse angles in point sets 

      Fabila Monroy, Ruy; Huemer, Clemens; Tramuns Figueras, Eulàlia (2013)
      In 1979 Conway, Croft, Erd\H{o}s and Guy proved that every set SS of nn points in general position in the plane determines ...
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      Guarding the vertices of thin orthogonal polygons is NP-hard 

      Nunes Gomes Tomás, Ana Paula (2013)
      An orthogonal polygon of P is called “thin” if the dual graph of the partition obtained by extending all edges of P towards ...
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      Distance domination, guarding and vertex cover for maximal outerplanar graphs 

      Canales Cano, Santiago; Hernández Peñalver, Gregorio; Oliveira Martins, Ana Mafalda de; Matos. Inês (2013)
      In this paper we de ne a distance guarding concept on plane graphs and associate this concept with distance domination and ...
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      Flips in combinatorial pointed pseudo-triangulations with face degree at most four 

      Aichholzer, Oswin; Hackl, Thomas; Orden Martín, David; Pilz, Alexander; Saumell Mendiola, María; Vogtenhuber, Birgit (2013)
      In this paper we consider the flip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or ...
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      On three parameters of invisibility graphs 

      Cibulka, Josef; Korbelář, Miroslav; Kynčl, Jan; Mészáros, Viola; Stolař, Rudolf; Valtr, Pavel (2013)
      The invisibility graph I(X) of a set X ⊆ Rd is a (possibly infinite) graph whose vertices are the points of X and two ...
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      Empty convex polytopes in random point sets 

      Balogh, József; González Aguilar, Hernán; Salazar Anaya, Gelasio (2013)
      Given a set P of points in Rd, a convex hole (alternatively, empty convex polytope) of P is a convex polytope with vertices ...
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      Some results on open edge guarding of polygons 

      Bajuelos Domínguez, António Leslie; Canales Cano, Santiago; Hernández Peñalver, Gregorio; Oliveira Martins, Ana Mafalda de; Matos. Inês (2013)
      This paper focuses on a variation of the Art Gallery problem that considers open edge guards. The “open” prefix means the ...
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      Improved enumeration of simple topological graphs 

      Kynčl, Jan (2013)
      A simple topological graph T = (V (T ), E(T )) is a drawing of a graph in the plane where every two edges have at most one ...
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      Stackable tessellations 

      Enrique Monzo, Lluís; Jaume Deyà, Rafel (2013)
      We introduce a class of solids that can be constructed gluing stackable pieces, which has been proven to have advantages ...