On the Monotone Upper Bound Problem

DOI10.1080/10586458.2004.10504519zbMath1068.52019arXivmath/0308186OpenAlexW2064917489MaRDI QIDQ4818674

Günter M. Ziegler, Julian Pfeifle

Publication date: 1 October 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0308186

zbMATH Keywords

convex polytopesmonotone pathsabstract objective functionsextended Gale diagramsupper bound problem

Mathematics Subject Classification ID

Computational aspects related to convexity (52B55) Linear programming (90C05) Enumeration in graph theory (05C30) Directed graphs (digraphs), tournaments (05C20) Gale and other diagrams (52B35)

Related Items

A Mihalisin-Klee theorem for fans, Long monotone paths on simple 4-polytopes, Monotone diameter of bisubmodular polyhedra, Random Walks on Polytopes of Constant Corank, Computing monotone disjoint paths on polytopes, Monotone Paths in Planar Convex Subdivisions and Polytopes, On the Length of Monotone Paths in Polyhedra

Uses Software

• polymake

Cites Work

• Unnamed Item
• Unnamed Item
• A simple way to tell a simple polytope from its graph
• Convex and linear orientations of polytopal graphs
• On the \(k\)-systems of a simple polytope
• Long monotone paths on simple 4-polytopes
• Lectures on Polytopes
• The number of simplicial neighbourly d ‐polytopes with d +3 vertices
• One line and ε
• Paths on Polyhedra. I
• The maximum numbers of faces of a convex polytope
• Entering and leaving \(j\)-facets