{"paper":{"title":"A note on hitting maximum and maximal cliques with a stable set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andrew D. King, Demetres Christofides, Katherine Edwards","submitted_at":"2011-09-14T14:34:19Z","abstract_excerpt":"It was recently proved that any graph satisfying $\\omega > \\frac 23(\\Delta+1)$ contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying $\\omega \\geq \\frac 23(\\Delta+1)$ unless the graph is the strong product of $K_{\\omega/2}$ and an odd hole. We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3092","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"}