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      Computing the stretch of an embedded graph 

      Cabello Justo, Sergio; Chimani, Markus; Hliněný, Petr (2013)
      Let G be a graph embedded in an orientable surface Σ, possibly with edge weights, and denote by len(γ) the length (the ...
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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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      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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      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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      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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      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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      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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      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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      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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      Metaheuristic approaches for the minimum dilation triangulation problem 

      Dorzán, María Gisela; Leguizamón, Mario Guillermo; Mezura Montes, Efrén; Hernández Peñalver, Gregorio (2013)
      We focus on the development of approximated algorithms to find high quality triangulations of minimum dilation because the ...
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      Monotone crossing number of complete graphs 

      Balko, Martin; Fulek, Radoslav; Kynčl, Jan (2013)
      In 1958, Hill conjectured that the minimum number of crossings in a drawing of Kn is exactly Z(n) = 1/4 n-1/2/2 n−2/2 ...
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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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      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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      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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      On the barrier-resilience of arrangements of ray-sensors 

      Kirkpatrick, David; Yang, Boting; Zilles, Sandra (2013)
      Given an arrangement A of n sensors and two points s and t in the plane, the barrier resilience of A with respect to s and ...
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      On the enumeration of permutominoes 

      Nunes Gomes Tomás, Ana Paula (2013)
      Although the exact counting and enumeration of polyominoes remain challenging open problems, several positive results were ...
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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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      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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      Parallel constrained Delaunay triangulation 

      Coll Arnau, Narcís; Guerrieri Basualdo, María Ethel (2013)
      In this paper we propose a new GPU method able to compute the 2D constrained Delaunay triangulation of a planar straight ...
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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 ...