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      Phase transitions in the Ramsey-Turán theory 

      Balogh, József (2013)
      Let f(n) be a function and L be a graph. Denote by RT(n, L, f(n)) the maximum number of edges of an L-free graph on n ...
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      On making a graph crossing-critical 

      Hernández Vélez, César Israel; Leaños Macías, Jesús (2013)
      A graph is crossing-critical if its crossing number decreases when we remove any of its edges. Recently it was proved that ...
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      Equipartitioning triangles 

      Ramos Alonso, Pedro Antonio; Steiger, William (2013)
      An intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for any positive integer ...
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      Continuous surveillance of points by rotating floodlights 

      Bereg, Sergey; Díaz Báñez, José Miguel; Fort i Masdevall, Marta; Lopez, Mario A.; Pérez Lantero, Pablo; Urrutia Galicia, Jorge (2013)
      Let P and F be sets of n ≥ 2 and m ≥ 2 points in the plane, respectively, so that P∪F is in general position. We study the ...
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      An algorithm that constructs irreducible triangulations of once-punctured surfaces 

      Chávez de Diego, María José; Lawrecenko, Serge; Portillo Fernández, José Ramón; Villar Liñán, María Trinidad (2013)
      A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the ...
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      Three location tapas calling for CG sauce 

      Plastria, Frank (2013)
      Based on some recent modelling considerations in location theory we call for study of three CG constructs of Voronoi type that seem not to have been studied much before.
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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 ...