Triangle Contact Representations and Duality

Goncalves, Daniel and Leveque, Benjamin and Pinlou, Alexandre (2011) Triangle Contact Representations and Duality. In: Graph Drawing 18th International Symposium, GD 2010, September 21-24, 2010 , pp. 262-273(Official URL: http://dx.doi.org/10.1007/978-3-642-18469-7_24).

Full text not available from this repository.

Abstract

A contact representation by triangles of a graph is a set of triangles in the plane such that two triangles intersect on at most one point, each triangle represents a vertex of the graph and two triangles intersects if and only if their corresponding vertices are adjacent. de Fraysseix, Ossona de Mendez and Rosenstiehl proved that every planar graph admits a contact representation by triangles. We strengthen this in terms of a simultaneous contact representation by triangles of a planar map and of its dual. A primal-dual contact representation by triangles of a planar map is a contact representation by triangles of the primal and a contact representation by triangles of the dual such that for every edge uv, bordering faces f and g, the intersection between the triangles corresponding to u and v is the same point as the intersection between the triangles corresponding to f and g. We prove that every 3-connected planar map admits a primal-dual contact representation by triangles. Moreover, the interiors of the triangles form a tiling of the triangle corresponding to the outer face and each contact point is a node of exactly three triangles. Then we show that these representations are in one-to-one correspondence with generalized Schnyder woods defined by Felsner for 3-connected planar maps.

Item Type: Conference Paper
Additional Information: 10.1007/978-3-642-18469-7_24
Classifications: Z Theory > Z.250 Geometry
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1212

Actions (login required)

View Item View Item