{"id":"W2964314221","doi":"10.11575/cdm.v12i2.62777","title":"Shellability, vertex decomposability, and lexicographical products of graphs","year":2015,"lang":"en","type":"article","venue":"University of Calgary","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University; Redeemer University","funders":"","keywords":"Lexicographical order; Combinatorics; Vertex (graph theory); Mathematics; Graph; Independence number; Product (mathematics); Discrete mathematics","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":[0.0003569177,0.00006904663,0.0002193939,0.0002260609,0.00003826795,0.000008172288,0.000596311,0.0000569579,0.00001692861],"category_scores_gemma":[0.0001671326,0.00006394164,0.0000708704,0.001235006,0.0004996484,0.0002151244,0.0006414597,0.00007230326,0.000002930588],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001048514,"about_ca_system_score_gemma":0.00005011351,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00051317,"about_ca_topic_score_gemma":0.00003726453,"domain_scores_codex":[0.999145,0.00008327082,0.0001209494,0.0002962335,0.0002386415,0.000115889],"domain_scores_gemma":[0.9990724,0.0001085111,0.00006557455,0.0004203497,0.0001912755,0.0001418666],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0001404203,0.001040328,0.5201159,0.0001363302,0.0001676398,0.00004399244,0.0009736225,0.00001912371,0.000488804,0.372244,0.002703269,0.1019266],"study_design_scores_gemma":[0.002207291,0.001277021,0.7164844,0.00003019273,0.0001644854,0.00002819187,0.0004938754,0.01033624,0.001611107,0.2522412,0.01458199,0.0005440033],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9578555,0.000320391,0.03716684,0.001376612,0.00007231407,0.0001048196,0.000007617798,0.00004743238,0.003048507],"genre_scores_gemma":[0.9789837,0.00003658977,0.02088697,0.00002200336,0.000002445191,3.146883e-8,0.000003923892,0.000001024023,0.00006331392],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1963686,"threshold_uncertainty_score":0.2607464,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02102381228144107,"score_gpt":0.2107784121309212,"score_spread":0.1897545998494802,"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."}}