{"id":"https://openalex.org/W7151265472","doi":"https://doi.org/10.1016/j.dam.2026.03.051","title":"Minimum degree of minimal <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e20\" altimg=\"si19.svg\"> <mml:mi>k</mml:mi> </mml:math> -factor-critical triangle-free graphs with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e25\" altimg=\"si20.svg\"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">\u2265</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>\u2212</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math>","display_name":"Minimum degree of minimal <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e20\" altimg=\"si19.svg\"> <mml:mi>k</mml:mi> </mml:math> -factor-critical triangle-free graphs with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e25\" altimg=\"si20.svg\"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">\u2265</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>\u2212</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math>","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7151265472","doi":"https://doi.org/10.1016/j.dam.2026.03.051"},"language":"en","primary_location":{"id":"doi:10.1016/j.dam.2026.03.051","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.dam.2026.03.051","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101527586","display_name":"Xiao Zhao","orcid":"https://orcid.org/0000-0003-0887-0003"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, PR China"],"raw_orcid":"https://orcid.org/0000-0003-0887-0003","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, PR China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053119997","display_name":"Yizhen Mao","orcid":null},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yizhen Mao","raw_affiliation_strings":["School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, PR China","institution_ids":["https://openalex.org/I75955062"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101527586"],"corresponding_institution_ids":["https://openalex.org/I75955062"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44555751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"388","issue":null,"first_page":"181","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.7427999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.7427999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.17870000004768372,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.02449999935925007,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5462999939918518},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5360000133514404},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4065999984741211},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.3521000146865845},{"id":"https://openalex.org/keywords/symmetric-graph","display_name":"Symmetric graph","score":0.34779998660087585},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.32440000772476196},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3224000036716461},{"id":"https://openalex.org/keywords/strongly-regular-graph","display_name":"Strongly regular graph","score":0.3206999897956848},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.3147999942302704}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8676000237464905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8629999756813049},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5462999939918518},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5360000133514404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5105000138282776},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.34779998660087585},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.32440000772476196},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C133875400","wikidata":"https://www.wikidata.org/wiki/Q692823","display_name":"Strongly regular graph","level":5,"score":0.3206999897956848},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.3147999942302704},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3109000027179718},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.29339998960494995},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.287200003862381},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.2615000009536743},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.2599000036716461},{"id":"https://openalex.org/C166911692","wikidata":"https://www.wikidata.org/wiki/Q7130424","display_name":"Pancyclic graph","level":5,"score":0.25699999928474426},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.25440001487731934},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2535000145435333},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.25200000405311584},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.dam.2026.03.051","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.dam.2026.03.051","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1970805731","https://openalex.org/W1985061810","https://openalex.org/W4376617939","https://openalex.org/W4389725887","https://openalex.org/W4393965438"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T06:08:40.794217","created_date":"2026-04-08T00:00:00"}
