The hirsch conjecture holds for normal flag complexes

Karim A. Adiprasito*, Bruno Benedetti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Using an intuition from metric geometry, we prove that any flag normal simplicial complex satisfies the nonrevisiting path conjecture. As a consequence, the diameter of its facet-ridge graph is smaller than the number of vertices minus the dimension, as in the Hirsch conjecture. This proves the Hirsch conjecture for all flag polytopes and, more generally, for all (connected) flag homology manifolds.

Original languageAmerican English
Pages (from-to)1340-1348
Number of pages9
JournalMathematics of Operations Research
Issue number4
StatePublished - 1 Nov 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
©2014 INFORMS.


  • Cat(1) spaces
  • Dual graph
  • Flag
  • Graph diameter
  • Hirsch conjecture
  • Polytopes
  • Simplex method


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