{"paper":{"title":"Max k-cut and the smallest eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. Nikiforov","submitted_at":"2016-04-07T17:50:03Z","abstract_excerpt":"Let $G$ be a graph of order $n$ and size $m$, and let $\\mathrm{mc}_{k}\\left( G\\right) $ be the maximum size of a $k$-cut of $G.$ It is shown that \\[ \\mathrm{mc}_{k}\\left( G\\right) \\leq\\frac{k-1}{k}\\left( m-\\frac{\\mu_{\\min }\\left( G\\right) n}{2}\\right) , \\] where $\\mu_{\\min}\\left( G\\right) $ is the smallest eigenvalue of the adjacency matrix of $G.$\n  An infinite class of graphs forcing equality in this bound is constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02088","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"}