{"id":"W107196105","doi":"","title":"On the Hall Number of a Graph.","year":2000,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Graph; Combinatorics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002809212,0.0000891257,0.00010682,0.00003280822,0.00009723905,0.00003637773,0.0006108595,0.00003907428,0.000218464],"category_scores_gemma":[0.00002383248,0.00005892333,0.00007110573,0.0004198815,0.00006370146,0.00008253819,0.00005035401,0.0001093754,0.0003621917],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005214554,"about_ca_system_score_gemma":0.00001951445,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005546394,"about_ca_topic_score_gemma":8.119863e-7,"domain_scores_codex":[0.9991542,0.00006905632,0.0001631741,0.000198483,0.0002481132,0.0001670322],"domain_scores_gemma":[0.9990326,0.000174227,0.00004830015,0.0006406401,0.00005577221,0.00004853021],"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":[0.000003470217,0.00008946365,0.0002636636,0.000001970285,0.000009151076,0.00000223317,0.0001557537,0.00001902094,0.00007842974,0.9920982,0.005585665,0.001693032],"study_design_scores_gemma":[0.0002719716,0.00005629607,0.000372067,0.00002068499,0.000002728553,0.000004612219,0.000003535584,0.0005993209,0.001131669,0.9968737,0.0005887644,0.0000746791],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9683016,0.00004888684,0.00002917267,0.001182056,0.0005364267,0.00008174787,5.676817e-7,0.00008682276,0.0297327],"genre_scores_gemma":[0.9983374,0.00001451007,0.0005594501,0.0005960768,3.965508e-7,0.000007228894,3.589788e-7,0.000005460682,0.0004790805],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03003582,"threshold_uncertainty_score":0.4655362,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01056716968773465,"score_gpt":0.2259312793497886,"score_spread":0.2153641096620539,"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."}}