The Hirsch Conjecture Holds for Normal Flag Complexes

• 成果类型: Article
• 署名作者: Adiprasito, Karim A.; Benedetti, Bruno
• 署名单位: Universite Paris Saclay
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0661
• 发表日期: 2014
• 页码: 1340-1348
• 关键词: d-step conjecture; diameter; polyhedra; graphs

摘要

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.