{"id":"W4411687204","doi":"10.61091/um123-09","title":"Path-systems in regular graphs and bipartite graphs","year":2025,"lang":"en","type":"article","venue":"Utilitas Mathematica","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Bipartite graph; Mathematics; Combinatorics; Path (computing); Chordal graph; Longest path problem; Discrete mathematics; Graph; Computer science; Computer network","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":[0.0009665937,0.0002216546,0.0004203075,0.0003520202,0.0001409002,0.0000589568,0.0002377149,0.0001212676,0.00005183803],"category_scores_gemma":[0.0003470588,0.0001948822,0.0001046816,0.0007767297,0.0002079413,0.00009636758,0.00008989174,0.000170123,0.00002884427],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001810142,"about_ca_system_score_gemma":0.00002342992,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001224193,"about_ca_topic_score_gemma":0.000010923,"domain_scores_codex":[0.9984174,0.0001352064,0.0005973589,0.0003555248,0.0001725018,0.0003220547],"domain_scores_gemma":[0.9983242,0.0006803023,0.0001085869,0.0007533415,0.00005120472,0.00008234254],"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":[0.00000942402,0.000215353,0.0004920495,0.0007304839,0.00004005035,0.000003347503,0.0006384153,4.001072e-7,0.0004470348,0.9944629,0.002522329,0.0004381985],"study_design_scores_gemma":[0.0003494025,0.00001792458,0.0006256165,0.0004314935,0.0000593307,0.000007956311,0.000926285,0.000724703,0.0002126191,0.994208,0.002269004,0.0001676433],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9683186,0.001695797,0.001328261,0.0006575033,0.0001172776,0.001219769,0.00003194808,0.0002705721,0.02636029],"genre_scores_gemma":[0.9937584,0.00005685327,0.00455708,0.0000650252,0.000005547639,0.0003626036,0.000004255298,0.00002263606,0.001167573],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02543984,"threshold_uncertainty_score":0.7947064,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02565338256795302,"score_gpt":0.2986187748509654,"score_spread":0.2729653922830124,"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."}}