{"id":"W4367048681","doi":"10.1016/j.disc.2023.113471","title":"The optimal bound on the 3-independence number obtainable from a polynomial-type method","year":2023,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Graph theory and applications","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Discrete mathematics; Independent set; Distance-regular graph; Independence number; Graph; Wheel graph; Upper and lower bounds; Hamming graph; Cubic graph; Graph power; Line graph; Voltage graph; Hamming code; Algorithm","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002057926,0.000260755,0.0002726883,0.00003748689,0.001138966,0.0002772782,0.0008610964,0.0001222599,0.0003169918],"category_scores_gemma":[0.00126784,0.0001416816,0.0001727598,0.0006613013,0.000193553,0.00007915023,0.0002074482,0.0003865545,0.001580524],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003455065,"about_ca_system_score_gemma":0.00005938411,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002496947,"about_ca_topic_score_gemma":0.00001287655,"domain_scores_codex":[0.9980724,0.0002223801,0.0004298185,0.0003050663,0.000493777,0.0004765726],"domain_scores_gemma":[0.9909394,0.0073702,0.0002288608,0.001278419,0.000100144,0.00008298922],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000203106,0.00005726082,0.00001369895,0.00002682983,0.00009051792,0.000004566228,0.002310263,0.00003465108,0.0004402135,0.9712514,0.02553055,0.0002197524],"study_design_scores_gemma":[0.0001461238,0.00002226214,0.00003427646,0.00005565596,0.00008504957,0.000007655302,0.005698612,0.006680536,0.002327419,0.9735152,0.01121584,0.0002113325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9104773,0.00005707211,0.02380813,0.008367864,0.0004499164,0.001831239,0.0001446877,0.0007765475,0.0540872],"genre_scores_gemma":[0.8874238,0.0001053155,0.08032553,0.0005681434,0.0004173589,0.0007105962,0.00005207266,0.0002188746,0.03017833],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0565174,"threshold_uncertainty_score":0.9991969,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05090655308444312,"score_gpt":0.3566939888169174,"score_spread":0.3057874357324743,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}