{"id":"W1802444145","doi":"10.37236/2698","title":"Product Dimension of Forests and Bounded Treewidth Graphs","year":2013,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Microsoft Research","keywords":"Combinatorics; Treewidth; Mathematics; Bounded function; Dimension (graph theory); Upper and lower bounds; Discrete mathematics; Graph; Product (mathematics); Partial k-tree; Chordal graph; Pathwidth; 1-planar graph; Line graph; Geometry","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":[0.002031411,0.0002969739,0.0006077669,0.0003262639,0.0001462699,0.0001428503,0.001542885,0.0001472946,0.000001607964],"category_scores_gemma":[0.0001158422,0.0001898742,0.0002230142,0.000479356,0.0001709574,0.0002221949,0.0008204235,0.001506392,0.000001661327],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000105939,"about_ca_system_score_gemma":0.0007963225,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004473817,"about_ca_topic_score_gemma":0.000006229554,"domain_scores_codex":[0.9973381,0.0002514706,0.0008120199,0.0003238154,0.0007274105,0.0005471502],"domain_scores_gemma":[0.9965296,0.0001772678,0.001447476,0.0009423591,0.000782838,0.0001204275],"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":[0.0000179592,0.0001391235,0.0003875039,0.0000668018,0.000146342,0.000003629259,0.0003449166,0.000145486,0.0004135018,0.9962704,0.0005930896,0.001471238],"study_design_scores_gemma":[0.0006194687,0.0005920192,0.0006085626,0.0001729302,0.00008582542,0.0001563812,0.00001026172,0.001437285,0.002869095,0.9930759,0.0001830425,0.0001891985],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9578745,0.03043496,0.007884265,0.001905355,0.001432829,0.0003427214,6.310654e-7,0.00003511464,0.0000895929],"genre_scores_gemma":[0.9966078,0.002734866,0.0004755372,0.00004757236,0.00001614959,0.000004837439,8.601766e-7,0.00001935184,0.00009304949],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03873324,"threshold_uncertainty_score":0.7742845,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009660454865182485,"score_gpt":0.2238191868941672,"score_spread":0.2141587320289847,"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."}}