{"paper":{"title":"Partitioning a graph into degenerate subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Carl Feghali, Faisal N. Abu-Khzam, Pinar Heggernes","submitted_at":"2018-03-12T17:29:28Z","abstract_excerpt":"Let $G = (V, E)$ be a connected graph with maximum degree $k\\geq 3$ distinct from $K_{k+1}$. Given integers $s \\geq 2$ and $p_1,\\ldots,p_s\\geq 0$, $G$ is said to be $(p_1, \\dots, p_s)$-partitionable if there exists a partition of $V$ into sets~$V_1,\\ldots,V_s$ such that $G[V_i]$ is $p_i$-degenerate for $i\\in\\{1,\\ldots,s\\}$. In this paper, we prove that we can find a $(p_1, \\dots, p_s)$-partition of $G$ in $O(|V| + |E|)$-time whenever $1\\geq p_1, \\dots, p_s \\geq 0$ and $p_1 + \\dots + p_s \\geq k - s$. This generalizes a result of Bonamy et al. (MFCS, 2017) and can be viewed as an algorithmic ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04388","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/1803.04388/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"}