{"id":"W2109408352","doi":"10.1016/j.disc.2015.10.008","title":"Triangle-free graphs with the maximum number of cycles","year":2015,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Combinatorics; Bipartite graph; Upper and lower bounds; Triangle-free graph; Pancyclic graph; Discrete mathematics; Graph; Complete bipartite graph; 1-planar graph; Chordal graph","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":[0.0008723985,0.0002656163,0.0005002486,0.00006058541,0.0001482048,0.0000393825,0.0008285863,0.00009908743,0.00009104258],"category_scores_gemma":[0.0006361687,0.0001322264,0.0001877074,0.000285501,0.0004211825,0.00009453583,0.000265234,0.0001914151,0.00001073252],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001685476,"about_ca_system_score_gemma":0.0000415113,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008172171,"about_ca_topic_score_gemma":0.00001460903,"domain_scores_codex":[0.9983333,0.0001040939,0.0004615921,0.0001903654,0.0006195038,0.0002911942],"domain_scores_gemma":[0.997309,0.0006876253,0.0003847255,0.001335255,0.0001668461,0.0001165948],"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":[0.00006062939,0.00007964447,0.0004426718,0.0002044572,0.0001534741,0.000006486994,0.00901692,0.000003679088,0.00001567504,0.9825642,0.007189318,0.0002629122],"study_design_scores_gemma":[0.001010219,0.00007136691,0.00005642231,0.00008852394,0.0001696448,0.00006728832,0.005624156,0.0001154377,0.0005056315,0.9913797,0.0007008444,0.0002107694],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8778123,0.0001435825,0.01007235,0.0007525071,0.0002244818,0.0007244594,0.00007807212,0.0001568323,0.1100354],"genre_scores_gemma":[0.9200686,0.000009587447,0.0788122,0.0000966329,0.00007993138,0.00003527888,0.000004931636,0.00008271702,0.0008101005],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1092253,"threshold_uncertainty_score":0.5392035,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0421209842775522,"score_gpt":0.3022750133111788,"score_spread":0.2601540290336267,"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."}}