{"id":"W3107865975","doi":"10.1002/jgt.22904","title":"A density bound for triangle‐free 4‐critical graphs","year":2022,"lang":"en","type":"article","venue":"Journal of Graph Theory","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Klein bottle; Mathematics; Combinatorics; Planar graph; Vertex (graph theory); Disjoint sets; Torus; Chordal graph; Projective plane; Discrete mathematics; Graph","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":[0.0006892367,0.0006587747,0.0006553106,0.001905512,0.001432939,0.00146231,0.001733262,0.001160867,0.0133274],"category_scores_gemma":[0.007997443,0.0006146403,0.0005266159,0.0009827282,0.002050465,0.002962419,0.00241917,0.001637695,0.0009193312],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001590216,"about_ca_system_score_gemma":0.0004964558,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002789246,"about_ca_topic_score_gemma":0.002174216,"domain_scores_codex":[0.9992334,0.0001090606,0.00001792275,0.0001285848,0.0002967182,0.0002144488],"domain_scores_gemma":[0.9928296,0.004702832,0.0004182071,0.0004631085,0.0007439677,0.0008422664],"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":[0.000322016,0.0001271541,0.006685677,0.0003637684,0.00005910129,0.0006957114,0.0009727366,0.03411756,0.02008132,0.9054093,0.01046805,0.02069763],"study_design_scores_gemma":[0.00005866244,0.0001187104,0.003662234,0.000133997,0.00006265618,0.001006544,0.0005275559,0.2071103,0.01221609,0.76145,0.01359686,0.00005638484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6558062,0.001927373,0.2345611,0.002851771,0.000200309,0.0001640586,0.0007234964,0.0006722727,0.1030935],"genre_scores_gemma":[0.9836137,0.000462253,0.01122366,0.0003381894,0.0000821843,0.00007263884,0.000304976,0.0001089268,0.003793416],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0133274,"threshold_uncertainty_score":0.04458457,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02714722103386607,"score_gpt":0.3144046545216235,"score_spread":0.2872574334877575,"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."}}