{"paper":{"title":"Almost balanced biased graph representations of frame matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daryl Funk, Matt DeVos","submitted_at":"2016-06-23T16:44:33Z","abstract_excerpt":"Given a 3-connected biased graph $\\Omega$ with a balancing vertex, and with frame matroid $F(\\Omega)$ nongraphic and 3-connected, we determine all biased graphs $\\Omega'$ with $F(\\Omega') = F(\\Omega)$. As a consequence, we show that if $M$ is a 4-connected nongraphic frame matroid represented by a biased graph $\\Omega$ having a balancing vertex, then $\\Omega$ essentially uniquely represents $M$. More precisely, all biased graphs representing $M$ are obtained from $\\Omega$ by replacing a subset of the edges incident to its unique balancing vertex with unbalanced loops."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07370","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"}