{"paper":{"title":"Tree-Residue Vertex-Breaking: a new tool for proving hardness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.CC","authors_text":"Erik D. Demaine, Mikhail Rudoy","submitted_at":"2017-06-24T03:32:42Z","abstract_excerpt":"In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph $G$ some of whose vertices are marked \"breakable,\" is it possible to convert $G$ into a tree via a sequence of \"vertex-breaking\" operations (replacing a degree-$k$ breakable vertex by $k$ degree-$1$ vertices, disconnecting the $k$ incident edges)?\n  We characterize the computational complexity of TRVB with any combination of the following additional constraints: $G$ must be planar, $G$ must be a simple graph, the degree of every breakable vertex must belong to an allowed list $B$, and the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07900","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"}