{"paper":{"title":"Tutte's 5-Flow Conjecture for Highly Cyclically Connected Cubic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eckhard Steffen","submitted_at":"2006-07-04T09:27:21Z","abstract_excerpt":"In 1954, Tutte conjectured that every bridgeless graph has a nowhere-zero 5-flow. Let $\\omega$ be the minimum number of odd cycles in a 2-factor of a bridgeless cubic graph. Tutte's conjecture is equivalent to its restriction to cubic graphs with $\\omega \\geq 2$. We show that if a cubic graph $G$ has no edge cut with fewer than $ {5/2} \\omega - 1$ edges that separates two odd cycles of a minimum 2-factor of $G$, then $G$ has a nowhere-zero 5-flow. This implies that if a cubic graph $G$ is cyclically $n$-edge connected and $n \\geq {5/2} \\omega - 1$, then $G$ has a nowhere-zero 5-flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607077","kind":"arxiv","version":2},"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"}