A counterexample to the Hirsch conjecture

Details A counterexample to the Hirsch conjecture A counterexample to the Hirsch conjecture

2010-06-14

arxiv.org/abs/1006.2814v3

Mathematics

Combinatorics

28 pages, 10 Figures: Changes from v2: Minor edits suggested by referees. This version has been accepted in the Annals of Math

Scientific paper

The Hirsch Conjecture (1957) stated that the graph of a $d$-dimensional polytope with $n$ facets cannot have (combinatorial) diameter greater than $n-d$. That is, that any two vertices of the polytope can be connected by a path of at most $n-d$ edges. This paper presents the first counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope with 48 facets which violates a certain generalization of the $d$-step conjecture of Klee and Walkup.

Affiliated with

Also associated with

No associations

Rating

A counterexample to the Hirsch conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A counterexample to the Hirsch conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A counterexample to the Hirsch conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423116