The Hirsch conjecture holds for normal flag complexes
Combinatorics
2014-04-14 v3 Metric Geometry
Optimization and Control
Abstract
Using an intuition from metric geometry, we prove that any flag and normal simplicial complex satisfies the non-revisiting 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.
Cite
@article{arxiv.1303.3598,
title = {The Hirsch conjecture holds for normal flag complexes},
author = {Karim Alexander Adiprasito and Bruno Benedetti},
journal= {arXiv preprint arXiv:1303.3598},
year = {2014}
}
Comments
9 pages, 1 figure; to appear in Mathematics of Operations Research