7 search results - page 1 / 2 » Convex and Linear Orientations of Polytopal Graphs |
DCG
2000
13 years 5 months ago
2000
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...
EJC
2000
13 years 5 months ago
2000
Consider the moment curve in the real Euclidean space Rd defined parametrically by the map : R Rd , t (t) = (t, t2 , . . . , td ). The cyclic d-polytope Cd(t1, . . . , tn) is t...
FOCS
2006
IEEE
13 years 11 months ago
2006
IEEE
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
DCG
2008
13 years 5 months ago
2008
In this paper we study connections between planar graphs, Schnyder woods, and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in gra...
SIAMDM
2010
12 years 12 months ago
2010
Inspired by the convex program of Eisenberg and Gale which captures Fisher markets with linear utilities, Jain and Vazirani [STOC, 2007] introduced the class of EisenbergGale (EG)...