{"id":"W1798981749","doi":"10.37236/999","title":"On the Quantum Chromatic Number of a Graph","year":2007,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":100,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada; University of Bristol","keywords":"Mathematics; Combinatorics; Chromatic scale; Discrete mathematics; Critical graph; Windmill graph; Friendship graph; Graph; Clique number; Quantum; Brooks' theorem; Graph power; Line graph; Quantum mechanics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.004197172,0.0001137388,0.0002022474,0.0001059106,0.0001501233,0.00003480129,0.001269704,0.00004196768,0.000006957782],"category_scores_gemma":[0.0001452229,0.00005611205,0.0001576924,0.0008714646,0.00008845272,0.0001039618,0.00006680362,0.0005843178,0.00001211689],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006609964,"about_ca_system_score_gemma":0.0002115191,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006279655,"about_ca_topic_score_gemma":0.000001207918,"domain_scores_codex":[0.9982278,0.0001415607,0.000495997,0.00008926017,0.0006106902,0.0004346424],"domain_scores_gemma":[0.9978218,0.0008295997,0.0005523761,0.0004793568,0.0002602292,0.00005664049],"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":[0.00001485363,0.000118249,0.00006357295,0.000004716468,0.00004723609,0.000004082195,0.0002861521,0.0000372082,0.0003953392,0.9981318,0.0006973477,0.0001995072],"study_design_scores_gemma":[0.0003790825,0.0004605622,0.0001681784,0.0000456509,0.00001927776,0.0001880179,0.00004643217,0.0006698661,0.003135105,0.9946373,0.0001840219,0.00006650636],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9095691,0.001405405,0.08478937,0.002544449,0.0006063349,0.0000965058,1.054804e-7,0.00002025026,0.0009685017],"genre_scores_gemma":[0.9994851,0.0001373822,0.00006141346,0.0002501386,0.000008492238,6.107051e-7,4.240193e-8,0.000007520905,0.00004925486],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08991607,"threshold_uncertainty_score":0.2538603,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008306689640085747,"score_gpt":0.2395849130024391,"score_spread":0.2312782233623534,"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."}}