{"paper":{"title":"Minimal Braces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcelo H. de Carvalho, Nishad Kothari, Phelipe A. Fabres","submitted_at":"2019-03-26T21:55:59Z","abstract_excerpt":"McCuaig (2001, Brace Generation, J. Graph Theory 38: 124-169) proved a generation theorem for braces, and used it as the principal induction tool to obtain a structural characterization of Pfaffian braces (2004, P{\\'o}lya's Permanent Problem, Electronic J. Combinatorics 11: R79).\n  A brace is minimal if deleting any edge results in a graph that is not a brace. From McCuaig's brace generation theorem, we derive our main theorem that may be viewed as an induction tool for minimal braces. As an application, we prove that a minimal brace of order $2n$ has size at most $5n-10$, when $n \\geq 6$, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11170","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.11170/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}