{"id":"W121029182","doi":"","title":"Application of Upper and Lower Bounds for the Domination Number to Vizing's Conjecture.","year":2003,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Conjecture; Domination analysis; Combinatorics; Upper and lower bounds; Mathematical analysis","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":[0.0004424604,0.00009788992,0.0001429988,0.00002817769,0.000185319,0.00002058792,0.0001157909,0.00007186577,0.00002302287],"category_scores_gemma":[0.0003789515,0.00006669739,0.0000536539,0.0001101832,0.00007040121,0.00004130668,0.00004138295,0.00006292121,0.000001776239],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001709386,"about_ca_system_score_gemma":0.00001163449,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003925205,"about_ca_topic_score_gemma":0.000001663156,"domain_scores_codex":[0.9993908,0.00004128076,0.0001772948,0.000145995,0.000121725,0.0001229487],"domain_scores_gemma":[0.9987469,0.0007350986,0.00008952359,0.0002929949,0.0001007807,0.00003470384],"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":[0.00002482444,0.00003306751,0.001116618,0.00003008754,0.00002819363,7.300778e-8,0.0006432158,0.000001004621,0.0003010504,0.9956396,0.0009382121,0.001244061],"study_design_scores_gemma":[0.0005374031,0.00004980521,0.001044046,0.000008010229,0.00004063421,0.000004208421,0.00008658785,0.0000582237,0.00393352,0.9831045,0.01104568,0.00008735203],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9870029,0.0000832006,0.006907618,0.0002346464,0.00113067,0.0008347866,0.000006996762,0.00002497709,0.003774224],"genre_scores_gemma":[0.9972096,0.000006000341,0.002412714,0.0001233185,0.000009034704,0.00008482928,0.000001223671,0.00001726746,0.0001359854],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01253506,"threshold_uncertainty_score":0.2719841,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01175639126937256,"score_gpt":0.2847729284611388,"score_spread":0.2730165371917663,"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."}}