{"paper":{"title":"Obstructions for partitioning into forests and outerplanar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ringi Kim, Sang-il Oum, Sergey Norin","submitted_at":"2019-03-20T10:27:30Z","abstract_excerpt":"For a class $\\mathcal C$ of graphs, we define $\\mathcal C$-edge-brittleness of a graph $G$ as the minimum $\\ell$ such that the vertex set of $G$ can be partitioned into sets inducing a subgraph in $\\mathcal C$ and there are $\\ell$ edges having ends in distinct parts. We characterize classes of graphs having bounded $\\mathcal C$-edge-brittleness for a class $\\mathcal C$ of forests or a class $\\mathcal C$ of graphs with no $K_4\\setminus e$ topological minors in terms of forbidden obstructions. We also define $\\mathcal C$-vertex-brittleness of a graph $G$ as the minimum $\\ell$ such that the edge "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.08425/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"}