{"id":"W2569250480","doi":"10.4230/lipics.stacs.2011.637","title":"Bounds on the maximum multiplicity of some common geometric graphs","year":2011,"lang":"en","type":"article","venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada; Deutsche Forschungsgemeinschaft; National Science Foundation","keywords":"Combinatorics; General position; Mathematics; Omega; Upper and lower bounds; Spanning tree; Multiplicity (mathematics); Regular polygon; Discrete mathematics; Geometry; Physics","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":[0.001629378,0.001717447,0.001427378,0.004069419,0.001645042,0.00260112,0.00366789,0.001498489,0.005758046],"category_scores_gemma":[0.01628612,0.000990438,0.001883121,0.003351253,0.002492373,0.007322671,0.004207827,0.00414891,0.001154502],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002569164,"about_ca_system_score_gemma":0.0006037177,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000741266,"about_ca_topic_score_gemma":0.0009222025,"domain_scores_codex":[0.9967237,0.0005410941,0.000190957,0.0009362203,0.001001979,0.000606044],"domain_scores_gemma":[0.9848305,0.007980219,0.002001787,0.002647509,0.001406636,0.001133325],"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":[0.0008245856,0.0002308421,0.01508781,0.0008652199,0.0003112766,0.0008389166,0.001130141,0.195858,0.04469528,0.6146014,0.007098671,0.1184579],"study_design_scores_gemma":[0.00004494698,0.0002611667,0.005858006,0.0001796356,0.0001865091,0.001280857,0.0003199187,0.4993122,0.02673721,0.448433,0.01725446,0.0001322038],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2871082,0.002502881,0.6634292,0.001307928,0.0001621038,0.0001385001,0.0008524819,0.0006481183,0.04385057],"genre_scores_gemma":[0.8535768,0.001697822,0.1360779,0.000223489,0.0003079319,0.0003259129,0.001074697,0.0002900311,0.006425444],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005758046,"threshold_uncertainty_score":0.01926261,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03768576974394765,"score_gpt":0.2456183393488825,"score_spread":0.2079325696049348,"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."}}