{"paper":{"title":"On the maximum number of maximum independent sets in connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Rautenbach, E. Mohr","submitted_at":"2018-06-27T11:59:00Z","abstract_excerpt":"We characterize the connected graphs of given order $n$ and given independence number $\\alpha$ that maximize the number of maximum independent sets. For $3\\leq \\alpha\\leq n/2$, there is a unique such graph that arises from the disjoint union of $\\alpha$ cliques of orders $\\left\\lceil\\frac{n}{\\alpha}\\right\\rceil$ and $\\left\\lfloor\\frac{n}{\\alpha}\\right\\rfloor$, by selecting a vertex $x$ in a largest clique and adding an edge between $x$ and a vertex in each of the remaining $\\alpha-1$ cliques. Our result confirms a conjecture of Derikvand and Oboudi [On the number of maximum independent sets of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10424","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":""},"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"}