{"id":"W4238782258","doi":"10.1002/jgt.20369","title":"On the chromatic number of a random 5‐regular graph","year":2009,"lang":"en","type":"article","venue":"Journal of Graph Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Combinatorics; Bounded function; Fractional coloring; Brooks' theorem; Chromatic scale; Discrete mathematics; Vertex (graph theory); Random graph; Critical graph; Graph; Graph power; Line graph; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.00338053,0.0002294264,0.0006014454,0.000199501,0.0002049369,0.00002398778,0.0006192793,0.0001123767,0.0004197131],"category_scores_gemma":[0.0009509418,0.0001075627,0.0007734047,0.00036258,0.0002652296,0.0001040982,0.00003140751,0.0004414206,0.000002746828],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001564456,"about_ca_system_score_gemma":0.00002637814,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":3.689323e-7,"about_ca_topic_score_gemma":2.99993e-7,"domain_scores_codex":[0.9975376,0.0006728222,0.0008507897,0.0001155808,0.000585073,0.0002381557],"domain_scores_gemma":[0.9950504,0.003247835,0.0009597802,0.0004583332,0.0001948872,0.00008878393],"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":[0.0008548443,0.0001862247,0.00006576446,0.00003512187,0.0002887419,0.00002291054,0.001190972,0.000006499924,0.001260853,0.9917054,0.002180535,0.002202136],"study_design_scores_gemma":[0.001385163,0.000314654,0.0008679578,0.0002606708,0.0001946287,0.0002588769,0.0003152324,0.00000451014,0.002510529,0.993639,0.00011398,0.0001347757],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9901327,0.0004177582,0.00168797,0.000371701,0.0003186728,0.000208233,0.000005378199,0.00001774,0.00683986],"genre_scores_gemma":[0.9978532,0.00009017975,0.001276707,0.0005475496,0.0001287307,0.000001788029,2.969768e-7,0.00001489541,0.00008666761],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007720498,"threshold_uncertainty_score":0.4595564,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01516593959118422,"score_gpt":0.2821104125560561,"score_spread":0.2669444729648719,"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."}}