{"id":"W2529549915","doi":"10.1016/j.ejc.2018.04.008","title":"Random 4-regular graphs have 3-star decompositions asymptotically almost surely","year":2018,"lang":"en","type":"preprint","venue":"European Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Counterexample; Combinatorics; Conjecture; Star (game theory); Graph; Discrete mathematics; Random graph; Asymptotically optimal algorithm; Planar graph; Random regular graph; Chordal graph; 1-planar 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.004855225,0.0006430132,0.001223814,0.0005207082,0.0005006876,0.000232082,0.001785093,0.0002537166,0.0001286709],"category_scores_gemma":[0.001152934,0.0005271044,0.001089824,0.0002301441,0.0004476164,0.0001300149,0.00115254,0.002216099,0.00002037831],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001237915,"about_ca_system_score_gemma":0.0001899712,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.076921e-7,"about_ca_topic_score_gemma":5.534018e-7,"domain_scores_codex":[0.9937866,0.002338473,0.001875203,0.0004167057,0.001083422,0.0004995578],"domain_scores_gemma":[0.9938593,0.000969886,0.001995018,0.001115132,0.001627651,0.0004330384],"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":[0.0006686601,0.0007889237,0.0009240384,0.0004768964,0.001750942,0.001713912,0.002135685,0.00010415,0.0001117555,0.9496494,0.04120629,0.0004693506],"study_design_scores_gemma":[0.003143229,0.0005876925,0.001389616,0.0007197587,0.0006829507,0.0004444737,0.00007644053,0.00006554791,0.000252103,0.9855717,0.006480901,0.0005855605],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8919234,0.002345922,0.04030445,0.0006582424,0.01402603,0.0007927229,0.0001114722,0.0001855383,0.0496522],"genre_scores_gemma":[0.9815994,0.0003786842,0.01648201,0.0001639543,0.000812695,0.000001890508,0.000014388,0.000207034,0.0003399717],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08967595,"threshold_uncertainty_score":0.9997181,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02950880662667421,"score_gpt":0.2848948329653568,"score_spread":0.2553860263386826,"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."}}