{"id":"https://openalex.org/W3082474995","doi":"https://doi.org/10.37236/8784","title":"Exact Minimum Codegree Thresholds for $K_4^-$-Covering and $K_5^-$-Covering","display_name":"Exact Minimum Codegree Thresholds for $K_4^-$-Covering and $K_5^-$-Covering","publication_year":2020,"publication_date":"2020-08-07","ids":{"openalex":"https://openalex.org/W3082474995","doi":"https://doi.org/10.37236/8784","mag":"3082474995"},"language":"en","primary_location":{"id":"doi:10.37236/8784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p22/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057874208","display_name":"Lei Yu","orcid":"https://orcid.org/0000-0003-0772-2914"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei Yu","raw_affiliation_strings":["School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068315573","display_name":"Xinmin Hou","orcid":"https://orcid.org/0000-0002-7634-0250"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinmin Hou","raw_affiliation_strings":["University of Science and Technology of China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100443141","display_name":"Yue Ma","orcid":"https://orcid.org/0009-0002-2299-4555"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Ma","raw_affiliation_strings":["School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101545201","display_name":"Boyuan Liu","orcid":"https://orcid.org/0009-0007-4163-6557"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Boyuan Liu","raw_affiliation_strings":["School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057874208"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":0.1027,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42567086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"27","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9002081155776978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8414814472198486},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5984414219856262},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5434702634811401},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4960990846157074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40944191813468933}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9002081155776978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8414814472198486},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5984414219856262},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5434702634811401},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4960990846157074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40944191813468933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/8784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/8784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3082474995.pdf","grobid_xml":"https://content.openalex.org/works/W3082474995.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W830927343","https://openalex.org/W2029416152","https://openalex.org/W2183769808","https://openalex.org/W2189228222","https://openalex.org/W2509966468","https://openalex.org/W2585665079","https://openalex.org/W3084146406","https://openalex.org/W4309682749"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W4288278856","https://openalex.org/W2572370460"],"abstract_inverted_index":{"Given":[0],"two":[1],"$3$-graphs":[2],"$F$":[3,16],"and":[4,64,79],"$H$,":[5],"an":[6,52,59],"$F$-covering":[7],"of":[8,13,15,23,32,62,76],"$H$":[9,18,24],"is":[10,25,84],"a":[11],"collection":[12],"copies":[14],"in":[17,27],"such":[19,41],"that":[20,42],"each":[21],"vertex":[22],"contained":[26],"at":[28],"least":[29],"one":[30,92],"copy":[31],"them.":[33],"Let":[34],"$c_2(n,F)$":[35],"be":[36],"the":[37,73,85],"minimum":[38,46],"integer":[39],"$t$":[40,50,89],"every":[43],"3-graph":[44],"with":[45,91],"codegree":[47],"greater":[48],"than":[49],"has":[51],"$F$-covering.":[53],"In":[54],"this":[55],"note,":[56],"we":[57],"answer":[58],"open":[60],"problem":[61],"Falgas-Ravry":[63],"Zhao":[65],"(SIAM":[66],"J.":[67],"Discrete":[68],"Math.,":[69],"2016)":[70],"by":[71],"determining":[72],"exact":[74],"value":[75],"$c_2(n,":[77,80],"K_4^-)$":[78],"K_5^-)$,":[81],"where":[82],"$K_t^-$":[83],"complete":[86],"$3$-graph":[87],"on":[88],"vertices":[90],"edge":[93],"removed.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
