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      Geometric tree graphs of points in convex position  [Article]

      Hernando, María del Carmen; Hurtado, Ferrán; Márquez Pérez, Alberto; Mora, Mercé; Noy, Marc (1999)
      Given a set P of points in the plane, the geometric tree graph of P is defined as the graph T(P) whose vertices are non-crossing spanning with straight edges trees of P, and where two trees T1 and T2 are adjacent if T2 = ...
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      Locally grid graphs: classification and Tutte uniqueness  [Article]

      Márquez Pérez, Alberto; Mier, Anna de; Noy, Marc; Revuelta Marchena, María Pastora (2003)
      We define a locally grid graph as a graph in which the structure around each vertex is a 3×3 grid ⊞, the canonical examples being the toroidal grids Cp×Cq. The paper contains two main results. First, we give a complete ...
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      Triangle-Free Planar Graphs as Segment Intersection Graphs  [Article]

      Castro Ochoa, Natalia de; Cobos Gavala, Javier; Dana Jiménez, Juan Carlos; Márquez Pérez, Alberto; Noy, Marc (2002)
      We prove that every triangle-free planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a ...
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      Triangle-Free Planar Graphs as Segments Intersection Graphs  [Article]

      Castro Ochoa, Natalia de; Cobos Gavala, Javier; Dana Jiménez, Juan Carlos; Márquez Pérez, Alberto; Noy, Marc (1999)
      We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a ...