{"id":"W4415614171","doi":"10.1016/j.disc.2025.114861","title":"The weak version of the graph complement conjecture and partial results for the delta conjecture","year":2025,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada; Pacific Institute for the Mathematical Sciences; American Institute of Mathematics","keywords":"Conjecture; Complement (music); Graph; Degeneracy (biology); Rank (graph theory); Graph property; Complement graph; Graph minor","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002604407,0.0008074871,0.001480843,0.00220958,0.003224543,0.004720217,0.002414089,0.002593241,0.01733716],"category_scores_gemma":[0.01044175,0.0006361045,0.001238074,0.002735559,0.00770465,0.01913579,0.005326892,0.006322954,0.001808712],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001723683,"about_ca_system_score_gemma":0.001081139,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002198713,"about_ca_topic_score_gemma":0.001663782,"domain_scores_codex":[0.9982638,0.0004803579,0.00008973655,0.0004749418,0.0004198076,0.0002713497],"domain_scores_gemma":[0.9893992,0.006349078,0.0005260437,0.001528188,0.001391748,0.0008058165],"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":[0.000126835,0.0000335538,0.000662964,0.0001182101,0.00001470737,0.00007645827,0.0001439967,0.0007899127,0.000416827,0.987645,0.004140249,0.005831293],"study_design_scores_gemma":[0.00001252259,0.000006387728,0.0001448396,0.00001566434,0.000007845016,0.00004168008,0.00007216165,0.001192654,0.0002406611,0.995998,0.002261799,0.000005717546],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3999225,0.004721727,0.2122218,0.06495535,0.002716745,0.0001061664,0.001532144,0.0005821876,0.3132414],"genre_scores_gemma":[0.9492546,0.002416883,0.01298471,0.004364212,0.001924762,0.00008444092,0.001336924,0.0001529277,0.02748063],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01733716,"threshold_uncertainty_score":0.0579986,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02528300008353636,"score_gpt":0.2918035087564597,"score_spread":0.2665205086729233,"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."}}