2013/03/14 by Karim Adiprasito, Bruno Benedetti, Adiprasito, Karim Alexander +1
Computer Science · Mathematics · #05C12 #05E45 #52B70 #53C21 #90C05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1303.3598
openalex publication_date 2013/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.