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» Estimating the number of vertices of a polyhedron
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IPL
2000
82views more  IPL 2000»
13 years 4 months ago
Estimating the number of vertices of a polyhedron
Given a polyhedron P by a list of inequalities we develop unbiased estimates of the number of vertices and bases of P. The estimates are based on applying tree estimation methods ...
David Avis, Luc Devroye
CCCG
2007
13 years 6 months ago
On the Fewest Nets Problem for Convex Polyhedra
Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edg...
Val Pinciu
ORL
2008
73views more  ORL 2008»
13 years 4 months ago
Polytopes and arrangements: Diameter and curvature
By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities de...
Antoine Deza, Tamás Terlaky, Yuriy Zinchenk...
RSA
2011
106views more  RSA 2011»
12 years 7 months ago
Distances between pairs of vertices and vertical profile in conditioned Galton-Watson trees
We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given leng...
Luc Devroye, Svante Janson
ARSCOM
2008
103views more  ARSCOM 2008»
13 years 5 months ago
Estimating the number of graphs containing very long induced paths
Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
Steven Butler