Convex Drawings of 3 - Conne ted Plane Graphs

Convex Drawings of Hierarchical Plane Graphs

This paper proves that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. This extends the previous known result that every hierarchical plane graph admits a straight-line drawing.

The Number of Labeled 2-Conne ted Planar Graphs

Beyond Outerplanarity

We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer k-planar graphs, where each edge is crossed by at most k other edges; and, outer k-quasi-planar graphs where no k edges can mutually cross. We show that the outer k-planar graphs are (b √ 4k + 1...

Minimum-Segment Convex Drawings of 3-Connected Cubic Plane Graphs

A convex drawing of a plane graph G is a plane drawing of G, where each vertex is drawn as a point, each edge is drawn as a straight line segment and each face is drawn as a convex polygon. A maximal segment is a drawing of a maximal set of edges that form a straight line segment. A minimum-segment convex drawing of G is a convex drawing of G where the number of maximal segments is the minimum ...

Convex Grid Drawings of 3-Connected Planar Graphs

We consider the problem of embedding the vertices of a plane graph into a small (polynomial size) grid in the plane in such a way that the edges are straight, non-intersecting line segments and faces are convex polygons. We present a linear-time algorithm which, given an n-vertex 3connected plane graph G (with n 3), nds such a straight-line convex embedding of G into a (n 2) (n 2) grid.