Nicolas Bonichon

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Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space. TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations introduced by Chew, have been shown(More)
We use Schnyder woods of 3-connected planar graphs to produce convex straight-line drawings on a grid of size $(n-2-\Delta)\times (n-2-\Delta).$ The parameter $\Delta\geq 0$ depends on the Schnyder wood used for the drawing. This parameter is in the range $0 \leq \Delta\leq {n}/{2}-2.$ The algorithm is a refinement of the face-counting algorithm; thus, in(More)
We consider the question: “What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph E?” The best known bound on the degree is 14. We show that E always contains a plane spanner of maximum degree 6 and stretch factor 6. This spanner can be constructed efficiently in linear time given the Triangular Distance Delaunay(More)
The family of well-orderly maps is a family of planar maps with the property that every connected planar graph has at least one plane embedding which is a well-orderly map.We show that the number of well-orderly maps with n nodes is at most 2αn+O(log , where α ≈ 4.91. A direct consequence of this is a new upper bound on the numberp(n) of unlabeled planar(More)
PURPOSE To evaluate the long-term results of external fractionated radiation therapy (RT) in the treatment of intracranial meningiomas. PATIENTS AND METHODS From January 1981 to December 1996, 156 patients with intracranial meningiomas were treated with external fractionated RT. Median age was 57. Indications for radiation therapy were as follows: (1)(More)