{"id":"W3092025494","doi":"10.1112/jlms.12781","title":"Sparse universal graphs for planarity","year":2023,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Agence Nationale de la Recherche","keywords":"Combinatorics; Mathematics; Planarity testing; Planar graph; Wheel graph; Vertex (graph theory); Hypercube graph; Discrete mathematics; Graph; Book embedding; Graph power; Line graph; Pathwidth","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":[0.0003165093,0.000444251,0.0005370621,0.001164,0.0009542978,0.001143457,0.0006834629,0.0005938669,0.0100268],"category_scores_gemma":[0.003884399,0.0003357278,0.0005591756,0.0009886067,0.001865968,0.002559473,0.003221581,0.001699481,0.0005389985],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009768277,"about_ca_system_score_gemma":0.0003404811,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001087162,"about_ca_topic_score_gemma":0.001175317,"domain_scores_codex":[0.9995315,0.0000931391,0.00001591355,0.000132191,0.0001189007,0.0001083456],"domain_scores_gemma":[0.9981738,0.0008157554,0.0002676813,0.0003146284,0.0002006367,0.0002274793],"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":[0.0000369389,0.00001649494,0.0004064196,0.00008039511,0.000009949284,0.00009968722,0.0001801393,0.006537869,0.001945065,0.9727134,0.002882685,0.015091],"study_design_scores_gemma":[0.00001663575,0.00002468335,0.0004170632,0.00003000652,0.000018339,0.0001851908,0.0001324245,0.0233287,0.001712387,0.9636546,0.01046856,0.00001127541],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4761479,0.001897397,0.3707261,0.004757667,0.0002785711,0.0001645443,0.0008645331,0.001217162,0.1439462],"genre_scores_gemma":[0.9691638,0.0006188041,0.02290785,0.0004685079,0.0001555659,0.00007136874,0.0003468121,0.00009271809,0.006174542],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0100268,"threshold_uncertainty_score":0.03354293,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03894361354742376,"score_gpt":0.3064994447618758,"score_spread":0.2675558312144521,"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."}}