{"paper":{"title":"The clique number and the smallest Q-eigenvalue of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla Oliveira, Leonardo de Lima, Vladimir Nikiforov","submitted_at":"2015-08-07T19:26:51Z","abstract_excerpt":"Let $q_{\\min}(G)$ stand for the smallest eigenvalue of the signless Laplacian of a graph $G$ of order $n.$ This paper gives some results on the following extremal problem:\n  How large can $q_\\min\\left( G\\right) $ be if $G$ is a graph of order $n,$ with no complete subgraph of order $r+1?$\n  It is shown that this problem is related to the well-known topic of making graphs bipartite. Using known classical results, several bounds on $q_{\\min}$ are obtained, thus extending previous work of Brandt for regular graphs.\n  In addition, using graph blowups, a general asymptotic result about the maximum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01784","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"}