{"id":"W4386857812","doi":"10.1016/j.procs.2023.08.244","title":"Graphs with constant balancing number","year":2023,"lang":"en","type":"article","venue":"Procedia Computer Science","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Combinatorics; Constant (computer programming); Edge coloring; Graph; Graph coloring; Computer science; Upper and lower bounds; Mathematics; Exponential function; Discrete mathematics; Line graph; Graph power","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":[0.0006448507,0.0001260541,0.000143852,0.0001443006,0.0004440918,0.0000991316,0.000504753,0.0000275016,0.00001901807],"category_scores_gemma":[0.00008496094,0.00008395573,0.00003161798,0.001585706,0.0006084523,0.000223116,0.0002872086,0.000111857,0.0000331313],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001807771,"about_ca_system_score_gemma":0.000115302,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001150376,"about_ca_topic_score_gemma":0.00000186949,"domain_scores_codex":[0.9985844,0.00001363382,0.0001498431,0.0003608524,0.0004854852,0.0004057683],"domain_scores_gemma":[0.9991766,0.0002017912,0.00006540906,0.0003036596,0.0001416061,0.0001109169],"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":[0.000008482472,0.00001500071,0.01655296,0.00007305227,0.00001057243,0.00002993947,0.002939969,0.00001626267,0.0001929446,0.9717864,0.00172001,0.006654393],"study_design_scores_gemma":[0.0002290872,0.00004777232,0.004634226,0.0000707638,0.000008373276,0.0001184813,0.00004919613,0.01012562,0.0008806313,0.9833779,0.00023706,0.0002208604],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.960785,0.00001163667,0.03136873,0.0001255734,0.0007775552,0.0002091173,0.000002732193,0.0005062301,0.006213439],"genre_scores_gemma":[0.9392172,0.000005041771,0.06042882,0.0001879024,0.000082675,0.000009601973,4.228195e-7,0.00001178163,0.00005657153],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0290601,"threshold_uncertainty_score":0.3423615,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01996392386131091,"score_gpt":0.2805415805631455,"score_spread":0.2605776567018346,"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."}}