{"id":"https://openalex.org/W4407084636","doi":"https://doi.org/10.1080/09728600.2024.2418640","title":"Sufficient conditions for the existence of path-factors with given properties","display_name":"Sufficient conditions for the existence of path-factors with given properties","publication_year":2025,"publication_date":"2025-01-02","ids":{"openalex":"https://openalex.org/W4407084636","doi":"https://doi.org/10.1080/09728600.2024.2418640"},"language":"en","primary_location":{"id":"doi:10.1080/09728600.2024.2418640","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2024.2418640","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2024.2418640?needAccess=true","source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2024.2418640?needAccess=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100586459","display_name":"Hui Qin","orcid":"https://orcid.org/0000-0002-8805-0015"},"institutions":[{"id":"https://openalex.org/I184681353","display_name":"Anhui University of Science and Technology","ror":"https://ror.org/00q9atg80","country_code":"CN","type":"education","lineage":["https://openalex.org/I184681353"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Qin","raw_affiliation_strings":["School of Mathematics and Big Data, Anhui University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Anhui University of Science and Technology","institution_ids":["https://openalex.org/I184681353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101846105","display_name":"Guowei Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CN","CZ"],"is_corresponding":false,"raw_author_name":"Guowei Dai","raw_affiliation_strings":["School of Mathematical Science & Institute of Mathematics, Nanjing Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science & Institute of Mathematics, Nanjing Normal University","institution_ids":["https://openalex.org/I152031979","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100400930","display_name":"Yuan Chen","orcid":"https://orcid.org/0000-0003-0086-1380"},"institutions":[{"id":"https://openalex.org/I4210119942","display_name":"Wuhan Textile University","ror":"https://ror.org/02jgsf398","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119942"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Chen","raw_affiliation_strings":["Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University","institution_ids":["https://openalex.org/I4210119942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079847773","display_name":"Ting Jin","orcid":"https://orcid.org/0000-0001-5383-2052"},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Jin","raw_affiliation_strings":["College of Science, Nanjing Forestry University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Nanjing Forestry University","institution_ids":["https://openalex.org/I167027274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100334768","display_name":"Yuan Yuan","orcid":"https://orcid.org/0000-0002-6458-9227"},"institutions":[{"id":"https://openalex.org/I20942203","display_name":"Hainan University","ror":"https://ror.org/03q648j11","country_code":"CN","type":"education","lineage":["https://openalex.org/I20942203"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuan Yuan","raw_affiliation_strings":["School of Science, Hainan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Hainan University","institution_ids":["https://openalex.org/I20942203"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5100334768"],"corresponding_institution_ids":["https://openalex.org/I20942203"],"apc_list":{"value":1000,"currency":"GBP","value_usd":1226},"apc_paid":{"value":1000,"currency":"GBP","value_usd":1226},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02403579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"1","first_page":"79","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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":0.9991000294685364,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8660718202590942},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5896420478820801},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5468336343765259},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06218728423118591}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8660718202590942},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5896420478820801},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5468336343765259},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06218728423118591},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/09728600.2024.2418640","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2024.2418640","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2024.2418640?needAccess=true","source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:607fe2d94b5745eb963c75d7d010b915","is_oa":true,"landing_page_url":"https://doaj.org/article/607fe2d94b5745eb963c75d7d010b915","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics, Vol 22, Iss 1, Pp 79-84 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/09728600.2024.2418640","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2024.2418640","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2024.2418640?needAccess=true","source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1424754290","display_name":null,"funder_award_id":"12201304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3990030799","display_name":null,"funder_award_id":"12201472, 12301441, 12201304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5757300161","display_name":null,"funder_award_id":"12201472","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6916910734","display_name":null,"funder_award_id":"12301441","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407084636.pdf","grobid_xml":"https://content.openalex.org/works/W4407084636.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W369866893","https://openalex.org/W1484040084","https://openalex.org/W1963596676","https://openalex.org/W2012966668","https://openalex.org/W2034647200","https://openalex.org/W2034949854","https://openalex.org/W2037953913","https://openalex.org/W2048484904","https://openalex.org/W2052963087","https://openalex.org/W2068431006","https://openalex.org/W2072174759","https://openalex.org/W2607117956","https://openalex.org/W2890163737","https://openalex.org/W2963505818","https://openalex.org/W2963730318","https://openalex.org/W2963781957","https://openalex.org/W2990898510","https://openalex.org/W2999068088","https://openalex.org/W3013246192","https://openalex.org/W3080270014","https://openalex.org/W3084642006","https://openalex.org/W3196602131","https://openalex.org/W4245743540","https://openalex.org/W4256646394","https://openalex.org/W4283464296","https://openalex.org/W4301586380","https://openalex.org/W4361253766","https://openalex.org/W4362578225","https://openalex.org/W6629141504","https://openalex.org/W6637360336","https://openalex.org/W6801002177"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"A":[0,34,52],"spanning":[1],"subgraph":[2],"H":[3,18],"of":[4,12,17,24],"a":[5,10,22,39,45,57,63,72,80,91,95,99,111,124,137,150],"graph":[6,35,41,53,59,73,92,97,113,126,139,152],"G":[7,13,36,54,109,122,135,148],"is":[8,19,31,37,55,74,110,123,136,149],"called":[9,38,56],"P\u2265k-factor":[11,46,64],"if":[14,42,60,71,114,127,140,153],"every":[15],"component":[16],"isomorphic":[20],"to":[21,93],"path":[23],"order":[25],"at":[26],"least":[27],"k,":[28],"where":[29],"k\u22652":[30],"an":[32],"integer.":[33],"(P\u2265k,l)-factor-critical":[40],"G\u2212V\u2032":[43],"contains":[44],"for":[47,65,90],"any":[48,66],"V\u2032\u2286V(G)":[49],"with":[50,68],"|V\u2032|=l.":[51],"(P\u2265k,m)-factor-deleted":[58],"G\u2212E\u2032":[61],"has":[62],"E\u2032\u2286E(G)":[67],"|E\u2032|=m.":[69],"Intuitively,":[70],"dense":[75],"enough,":[76],"it":[77],"will":[78],"have":[79],"P\u22653-factor.":[81],"In":[82,102],"this":[83,103],"paper,":[84,104],"we":[85,105],"give":[86],"some":[87],"sufficient":[88],"conditions":[89],"be":[94],"(P\u22653,l)-factor-critical":[96,112,125],"or":[98],"(P\u22653,m)-factor-deleted":[100,138,151],"graph.":[101],"demonstrate":[106],"that":[107],"(i)":[108],"its":[115,128,141,154],"sun":[116,142],"toughness":[117,143],"s(G)>l+13":[118],"and":[119,132,145,158],"\u03ba(G)\u2265l+2.":[120],"(ii)":[121],"degree":[129,155],"sum":[130,156],"\u03c33(G)\u2265n+2l":[131],"\u03ba(G)\u2265l+1.":[133],"(iii)":[134],"s(G)\u2265m+1m+2":[144],"\u03ba(G)\u22652m+1.":[146,159],"(iv)":[147],"\u03c33(G)\u2265n+2m":[157]},"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
