{"paper":{"title":"Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Michael A. Henning, Michael Gentner","submitted_at":"2015-07-16T16:54:05Z","abstract_excerpt":"For a sequence $d$ of non-negative integers, let ${\\cal F}(d)$ be the set of all forests whose degree sequence is $d$. We present closed formulas for $\\gamma_{\\max}^{\\cal F}(d)=\\max\\{ \\gamma(F):F\\in {\\cal F}(d)\\}$ and $\\alpha_{\\min}^{\\cal F}(d)=\\min\\{ \\alpha(F):F\\in {\\cal F}(d)\\}$ where $\\gamma(F)$ and $\\alpha(F)$ are the domination number and the independence number of a forest $F$, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04650","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"}