{"id":"W4390937016","doi":"10.1090/mcom/3943","title":"Few hamiltonian cycles in graphs with one or two vertex degrees","year":2024,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Dawson College","funders":"KU Leuven; Fonds Wetenschappelijk Onderzoek; Natural Sciences and Engineering Research Council of Canada; Vlaamse regering; Japan Society for the Promotion of Science; Onderzoeksraad, KU Leuven; Vlaams Supercomputer Centrum","keywords":"Vertex (graph theory); Combinatorics; Hamiltonian (control theory); Hamiltonian path; Mathematics; Hamiltonian path problem; Graph; Mathematical optimization","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0005322638,0.0004767912,0.0006899018,0.001264058,0.001360766,0.001780947,0.00130115,0.00089844,0.005359817],"category_scores_gemma":[0.006680126,0.0007706621,0.0007202812,0.001242178,0.001846323,0.002992173,0.001272331,0.001284693,0.0006243545],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0010327,"about_ca_system_score_gemma":0.0006142228,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001323021,"about_ca_topic_score_gemma":0.002382581,"domain_scores_codex":[0.9993131,0.0001592584,0.00003672657,0.0002781166,0.00009998019,0.0001129013],"domain_scores_gemma":[0.9943046,0.003703061,0.0006498263,0.0006326241,0.0002900643,0.0004198832],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0007469616,0.0002211624,0.01418266,0.001449917,0.0002482613,0.001328024,0.002077968,0.06229692,0.02773205,0.7959555,0.01331731,0.08044325],"study_design_scores_gemma":[0.0001059557,0.0001140622,0.002558172,0.0001203823,0.0001261806,0.0008092125,0.0006203072,0.08197093,0.008296512,0.8952765,0.009957263,0.00004458065],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8320507,0.001853957,0.1378707,0.002541388,0.0001032411,0.000103034,0.001239934,0.0005316548,0.02370541],"genre_scores_gemma":[0.9576035,0.000695977,0.03413418,0.0004302166,0.00008730243,0.00009830383,0.0008493265,0.0001238224,0.005977432],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005359817,"threshold_uncertainty_score":0.01793039,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03130157513689866,"score_gpt":0.2807987119287609,"score_spread":0.2494971367918623,"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."}}