{"paper":{"title":"The Diameters of Network-flow Polytopes satisfy the Hirsch Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Finhold, J. A. De Loera, S. Borgwardt","submitted_at":"2016-03-01T15:39:38Z","abstract_excerpt":"We solve a problem in the combinatorics of polyhedra motivated by the network simplex method. We show that the Hirsch conjecture holds for the diameter of the graphs of all network-flow polytopes, in particular the diameter of a network-flow polytope for a network with $n$ nodes and $m$ arcs is never more than $m+n-1$. A key step to prove this is to show the same result for classical transportation polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00325","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}