Nicolas Bonichon

Convex Drawings of 3-Connected Plane Graphs

AbstractWe use Schnyder woods of 3-connected planar graphs to produce convex straight-line drawings on a grid of size

Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces

(n-2-\Delta)\times (n-2-\Delta).

Intervals in Catalan lattices and realizers of triangulations

The parameter

An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation

\Delta\geq 0

Wagner's Theorem on Realizers

depends on the Schnyder wood used for the drawing. This parameter is in the range

Convex drawings of 3-connected plane graphs

0 \leq \Delta\leq {n}/{2}-2.

BAXTER PERMUTATIONS AND PLANE BIPOLAR ORIENTATIONS

The algorithm is a refinement of the face-counting algorithm; thus, in particular, the size of the grid is at most

Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation

(f-2)\times(f-2).

Scheduling divisibleworkloads on heterogeneous platforms under bounded multi-port model

The above bound on the grid size simultaneously matches or improves all previously known bounds for convex drawings, in particular Schnyders and the recent Zhang and He bound for triangulations and the Chrobak and Kant bound for 3-connected planar graphs. The algorithm takes linear time. The drawing algorithm has been implemented and tested. The expected grid size for the drawing of a random triangulation is close to

Watermelon uniform random generation with applications

\frac{7}{8}n\times\frac{7}{8}n.