{"id":"W4390575946","doi":"10.1137/1.9781611977912.46","title":"Random Embeddings of Graphs: The Expected Number of Faces in Most Graphs is Logarithmic","year":2024,"lang":"en","type":"book-chapter","venue":"Society for Industrial and Applied Mathematics eBooks","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Random graph; Chordal graph; Indifference graph; Random regular graph; Mathematics; Combinatorics; Pathwidth; Maximal independent set; Embedding; 1-planar graph; Discrete mathematics; Logarithm; Graph; Line graph; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001419103,0.0006881649,0.0009562807,0.0008662484,0.0008707768,0.00263042,0.001663808,0.001767397,0.005708911],"category_scores_gemma":[0.01316435,0.0006039111,0.0007605351,0.0010316,0.002444199,0.00604093,0.001203385,0.002302247,0.001163726],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001386352,"about_ca_system_score_gemma":0.0003557812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005386788,"about_ca_topic_score_gemma":0.0006972958,"domain_scores_codex":[0.9991598,0.0002147789,0.00002588776,0.0002912029,0.0002144758,0.00009383157],"domain_scores_gemma":[0.9912155,0.00618729,0.0007201974,0.00122859,0.000273894,0.0003745503],"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":[0.0004799935,0.0001221805,0.01073812,0.0006719868,0.0001669465,0.0005321961,0.0004635047,0.1041826,0.007229564,0.7433329,0.0323102,0.09976982],"study_design_scores_gemma":[0.00003954507,0.00007639206,0.003849345,0.00008329213,0.00004868805,0.0007867953,0.0001033515,0.1337473,0.003303774,0.8470246,0.01090023,0.0000366517],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.4408288,0.007190517,0.477483,0.01176951,0.0005349075,0.000183906,0.002821631,0.00202789,0.05715984],"genre_scores_gemma":[0.9318349,0.004121315,0.04017551,0.001305237,0.0004869854,0.000364053,0.001726198,0.0005844861,0.01940121],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.005708911,"threshold_uncertainty_score":0.01909816,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04582269644482025,"score_gpt":0.289255121712687,"score_spread":0.2434324252678668,"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."}}