## Find a copy in the library

Finding libraries that hold this item...

## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Victor Klee; David W Walkup; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB. |

OCLC Number: | 227397643 |

Notes: | Also available from the authors. |

Description: | 47 p. |

### Abstract:

Two functions A and B, of interest in combinatorial geometry and the theory of linear programming, are defined and studied. A(d, n) is the maximum diameter of convex polyhedra of dimension d with n faces of dimension d-1; similarly, B(d, n) is the maximum diameter of bounded polyhedra of dimension d with n faces of dimension d-1. The diameter of a polyhedron P is the smallest integer k such that any two vertices of P can be joined by a path of k or fewer edges of P. It is shown that the bounded d-step conjecture, i.e. B(d,2d) = d, is true for d <or 5. It is also shown that the general d-step conjecture, i.e. A(d,2d) <or = d, of significance in linear programming, is false for d equal to or greater than 4. A number of other specific values and bounds for A and B are presented.

## Reviews

*User-contributed reviews*

Add a review and share your thoughts with other readers.
Be the first.

Add a review and share your thoughts with other readers.
Be the first.

## Tags

Add tags for "The d-step conjecture for polyhedra of dimension d<6.".
Be the first.