Hirsch Conjecture

Francisco Santos has announced a counterexample to the Hirsch conjecture:

“I will describe the construction of a 43-dimensional polytope with 86 facets and diameter bigger than 43. The proof is based on a generalization of the $d$-step theorem of Klee and Walkup.”

The above is from this website:
https://sites.google.com/a/alaska.edu/kleegrunbaum/

In July the result will presented at a conference in Seattle. More information is available at the above website.

The question of a polynomial upper bound is still open: http://gilkalai.wordpress.com/2010/05/10/francisco-santos-disproves-the-hirsch-conjecture/#comment-3040
http://personales.unican.es/santosf/
“I am afraid my construction says nothing about the polynomiality. As far as I know $2n-2$ (for example) could still be an upper bound for the diameter.”

The question of polynomiality could still be the subject of Polymath3 as that question is open.

I heard about this here:
http://gilkalai.wordpress.com/2010/05/10/francisco-santos-disproves-the-hirsch-conjecture/#comment-3041

Francisco Santos has a website here:
http://personales.unican.es/santosf/

Congratulations to him for solving this!

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One Response to “Hirsch Conjecture”

  1. Rumor: Pegatron Tapped For CDMA IPhone Manufacture Says:

    […] Hirsch Conjecture « Euclidean Ramsey Theory […]

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