The hirsch conjecture holds for normal flag complexes

Karim A. Adiprasito; Bruno Benedetti

doi:10.1287/moor.2014.0661

The hirsch conjecture holds for normal flag complexes

Karim A. Adiprasito^*, Bruno Benedetti

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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 language	English
Pages (from-to)	1340-1348
Number of pages	9
Journal	Mathematics of Operations Research
Volume	39
Issue number	4
DOIs	https://doi.org/10.1287/moor.2014.0661
State	Published - 1 Nov 2014
Externally published	Yes

Bibliographical note

Publisher Copyright:
©2014 INFORMS.

Keywords

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

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KW - Graph diameter

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KW - Polytopes

KW - Simplex method

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The hirsch conjecture holds for normal flag complexes

Abstract

Bibliographical note

Keywords

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