{"paper":{"title":"Induced and Weak Induced Arboricities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich, Philip D\\\"orr, Torsten Ueckerdt","submitted_at":"2018-03-06T13:02:51Z","abstract_excerpt":"We define the induced arboricity of a graph $G$, denoted by ${\\rm ia}(G)$, as the smallest $k$ such that the edges of $G$ can be covered with $k$ induced forests in $G$. This notion generalizes the classical notions of the arboricity and strong chromatic index.\n  For a class $\\mathcal{F}$ of graphs and a graph parameter $p$, let $p(\\mathcal{F}) = \\sup\\{p(G) \\mid G\\in \\mathcal{F}\\}$. We show that ${\\rm ia}(\\mathcal{F})$ is bounded from above by an absolute constant depending only on $\\mathcal{F}$, that is ${\\rm ia}(\\mathcal{F})\\neq\\infty$ if and only if $\\chi(\\mathcal{F} \\nabla \\frac{1}{2}) \\ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02152","kind":"arxiv","version":1},"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"}