{"id":"W3198893576","doi":"10.5802/alco.169","title":"The Erdős–Ko–Rado theorem for 2-intersecting families of perfect matchings","year":2021,"lang":"en","type":"article","venue":"Algebraic Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Perfect graph theorem; Mathematics; Vertex (graph theory); Matching (statistics); Graph; Perfect graph; Strong perfect graph theorem; Extension (predicate logic); Discrete mathematics; Line graph; Computer science; Graph power; Pathwidth","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002347672,0.000746899,0.001829122,0.003001513,0.002935943,0.002805652,0.001542507,0.00170876,0.008625221],"category_scores_gemma":[0.01151216,0.0008387655,0.001803155,0.002579256,0.001993256,0.007876629,0.003092387,0.002420882,0.001496396],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001934191,"about_ca_system_score_gemma":0.0009712629,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00151526,"about_ca_topic_score_gemma":0.0006351459,"domain_scores_codex":[0.9968944,0.000599979,0.0002324188,0.0009716059,0.0007293117,0.0005723194],"domain_scores_gemma":[0.9935554,0.003597796,0.0009056371,0.0007706344,0.0007569198,0.0004136078],"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":[0.000160025,0.00003745592,0.001581435,0.0002044839,0.00006326049,0.0003132767,0.0004391407,0.008125967,0.001281105,0.9621041,0.004987576,0.02070219],"study_design_scores_gemma":[0.0000583478,0.00007795425,0.001158858,0.00008689635,0.00006891436,0.0009475173,0.0002731692,0.03085579,0.001232057,0.9439171,0.0212709,0.00005245598],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3741444,0.005674092,0.4694556,0.004368602,0.0004550716,0.0002141785,0.002814544,0.0008943607,0.1419791],"genre_scores_gemma":[0.9294037,0.004691066,0.04518085,0.001041498,0.0005353588,0.0004553665,0.001666649,0.0001327202,0.01689276],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008625221,"threshold_uncertainty_score":0.02885419,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02013845099307112,"score_gpt":0.2860455054698701,"score_spread":0.265907054476799,"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."}}