PATHS IN POLYHEDRA. I,
Abstract
Further study was made into the behavior of paths in polyhedra relative to the number of facets. Section I, on longest simple paths and circuits, asserts that polytopes which are 'polar' (or 'combinatorially dual') to the cyclic polytopes all admit Hamiltonian circuits. This leads to a sharp upper bound for the lengths of simple paths admitted by polyhedra of given dimension and having a given number of facets. Section II is devoted to the conjecture that any 2 vertices of a polyhedron can be joined by a path therein which never returns to a facet from which it has departed earlier. The conjecture is proved for 3-dimensional polyhedra, and a stronger form (dealing with polyhedral cell complexes) is established for special cases.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1964
- Accession Number
- AD0609571
Entities
People
- Victor Klee
Organizations
- Boeing