{"id":"W2407621886","doi":"","title":"The Independence Number of the Cartesian Product of Graphs.","year":2011,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Cartesian product; Mathematics; Independence (probability theory); Independence number; Product (mathematics); Combinatorics; Discrete mathematics; Arithmetic; Statistics; Geometry; Graph","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006011056,0.00009211875,0.0001252456,0.00002711005,0.000164937,0.00001810286,0.001360692,0.00004015515,0.000005120037],"category_scores_gemma":[0.000082367,0.00005107601,0.00008805611,0.000600535,0.0002325521,0.0001259504,0.0002776415,0.0001461981,0.000009073331],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005272153,"about_ca_system_score_gemma":0.00007666028,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002121226,"about_ca_topic_score_gemma":0.000008578391,"domain_scores_codex":[0.9988398,0.0001078029,0.0002674878,0.0002151118,0.0003836891,0.0001861229],"domain_scores_gemma":[0.9983201,0.00007223209,0.0002069359,0.001118734,0.0002416116,0.00004036159],"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":[0.000002640414,0.00006166675,0.03068115,0.000006686323,0.00001345741,5.736433e-7,0.000758461,6.878182e-7,0.0006093602,0.9666443,0.0004065288,0.0008144887],"study_design_scores_gemma":[0.000176571,0.00003171462,0.02030339,0.00002403566,0.000006622626,0.000006987166,0.00002442661,0.0000687783,0.03824318,0.940965,0.00008307699,0.0000661973],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9915435,0.0002703751,0.00002843343,0.0003103984,0.002311703,0.0001814943,7.194973e-7,0.00004272222,0.005310606],"genre_scores_gemma":[0.9990243,0.00001435124,0.0008102183,0.00003628609,4.297249e-7,0.000006794314,8.163402e-8,0.000005266449,0.0001022377],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03763382,"threshold_uncertainty_score":0.2528527,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01482391960570695,"score_gpt":0.221288058923668,"score_spread":0.2064641393179611,"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."}}