{"id":"W1001014873","doi":"10.1016/j.disc.2015.04.021","title":"New bounds for chromatic polynomials and chromatic roots","year":2015,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Chromatic scale; Upper and lower bounds; Graph; Chromatic polynomial; Order (exchange); Discrete mathematics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006633639,0.005140723,0.003317595,0.01279099,0.004641456,0.0109161,0.009007646,0.003956044,0.03633719],"category_scores_gemma":[0.04308255,0.0023124,0.002965556,0.01172998,0.009698987,0.03037998,0.01314997,0.02409179,0.008103053],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.007874322,"about_ca_system_score_gemma":0.002070392,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003151727,"about_ca_topic_score_gemma":0.005698456,"domain_scores_codex":[0.9946767,0.0009448664,0.0002165482,0.001246953,0.00196499,0.000949898],"domain_scores_gemma":[0.9668081,0.02297365,0.001566734,0.003211563,0.003011477,0.002428524],"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":[0.0001322355,0.0001042174,0.0005047586,0.0002753132,0.000036851,0.00007391842,0.0003455718,0.004514201,0.001259496,0.9448507,0.01605272,0.03184999],"study_design_scores_gemma":[0.00001895689,0.00002133628,0.0003900395,0.00009425067,0.00005083211,0.0000788992,0.00008356472,0.01342413,0.0005207449,0.9726943,0.01258034,0.00004270161],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03617794,0.01884953,0.6520347,0.01774937,0.004614736,0.0001950304,0.001622501,0.001811964,0.2669442],"genre_scores_gemma":[0.5906733,0.02322348,0.2383047,0.008587371,0.01674769,0.001125384,0.003177414,0.003342138,0.1148186],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03633719,"threshold_uncertainty_score":0.12156,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06934156671547613,"score_gpt":0.3475302862876567,"score_spread":0.2781887195721806,"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."}}