{"paper":{"title":"Generating Near-Bipartite Bricks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nishad Kothari","submitted_at":"2016-11-23T17:35:28Z","abstract_excerpt":"A $3$-connected graph $G$ is a brick if, for any two vertices $u$ and $v$, the graph $G-\\{u,v\\}$ has a perfect matching. Deleting an edge $e$ from a brick $G$ results in a graph with zero, one or two vertices of degree two. The bicontraction of a vertex of degree two consists of contracting the two edges incident with it; and the retract of $G-e$ is the graph $J$ obtained from it by bicontracting all its vertices of degree two. An edge $e$ is thin if $J$ is also a brick. Carvalho, Lucchesi and Murty [How to build a brick, Discrete Mathematics 306 (2006), 2383-2410] showed that every brick, dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07899","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"}