{"id":"W2782559833","doi":"10.1016/j.dam.2017.12.025","title":"On the b-chromatic number of cartesian products","year":2018,"lang":"en","type":"article","venue":"Discrete Applied Mathematics","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa; University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; University of Ottawa","keywords":"Cartesian product; Chromatic scale; Mathematics; Combinatorics; Cartesian coordinate system; Product (mathematics); Upper and lower bounds; Degree (music); Discrete mathematics; Geometry; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.0005760152,0.0001603441,0.0002173856,0.00005423862,0.0001535512,0.00005841891,0.001251909,0.00003927137,0.00007343796],"category_scores_gemma":[0.0002124636,0.00009819052,0.00004904925,0.0006215053,0.0003916915,0.00009732889,0.000271313,0.0001398706,0.0005490964],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001797792,"about_ca_system_score_gemma":0.00004080419,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.445824e-7,"about_ca_topic_score_gemma":7.120291e-7,"domain_scores_codex":[0.998556,0.00003551616,0.0002974441,0.0002867936,0.0005104615,0.0003137597],"domain_scores_gemma":[0.9976494,0.000498699,0.0001666484,0.00150757,0.0001202515,0.00005747683],"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":[0.000004338699,0.0000584072,0.000002948738,0.00008223393,0.00001749858,9.136132e-7,0.002137205,0.000002542986,0.005698491,0.9908606,0.0004557957,0.0006789829],"study_design_scores_gemma":[0.0001398584,0.00006268867,0.00002512455,0.00005257087,0.000007087856,0.000008756366,0.0002616995,0.004597573,0.06947578,0.925082,0.0001456223,0.0001412323],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.183566,0.00001213444,0.6381361,0.001407782,0.0001284956,0.001209181,0.000005975831,0.0002070798,0.1753272],"genre_scores_gemma":[0.8602204,0.000001383254,0.139336,0.0001218122,0.00004603568,0.00005862448,8.835416e-7,0.00001995183,0.0001949326],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6766543,"threshold_uncertainty_score":0.7057707,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02171155502913312,"score_gpt":0.2943312607134387,"score_spread":0.2726197056843056,"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."}}