{"id":"https://openalex.org/W4292547926","doi":"https://doi.org/10.3390/axioms11080417","title":"The Independence Number Conditions for 2-Factors of a Claw-Free Graph","display_name":"The Independence Number Conditions for 2-Factors of a Claw-Free Graph","publication_year":2022,"publication_date":"2022-08-19","ids":{"openalex":"https://openalex.org/W4292547926","doi":"https://doi.org/10.3390/axioms11080417"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11080417","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080417","pdf_url":"https://www.mdpi.com/2075-1680/11/8/417/pdf?version=1660891556","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/8/417/pdf?version=1660891556","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055644262","display_name":"Wanpeng Lei","orcid":"https://orcid.org/0000-0003-3701-9437"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I174104030","display_name":"Taiyuan Normal University","ror":"https://ror.org/051k00p03","country_code":"CN","type":"education","lineage":["https://openalex.org/I174104030"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wanpeng Lei","raw_affiliation_strings":["Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China","School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China","institution_ids":["https://openalex.org/I174104030"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031762495","display_name":"Liming Xiong","orcid":"https://orcid.org/0000-0002-3091-3252"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liming Xiong","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113606091","display_name":"Jun Yin","orcid":"https://orcid.org/0009-0005-9397-8941"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Yin","raw_affiliation_strings":["School of Computer Science, Qinghai Normal University, Xining 810008, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Qinghai Normal University, Xining 810008, China","institution_ids":["https://openalex.org/I20616075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055644262"],"corresponding_institution_ids":["https://openalex.org/I125839683","https://openalex.org/I174104030"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11386531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"8","first_page":"417","last_page":"417"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994000196456909,"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":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8151466846466064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6780349016189575},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.5196325182914734},{"id":"https://openalex.org/keywords/claw","display_name":"Claw","score":0.4853290617465973},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45216476917266846},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.451654314994812},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3431187868118286},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.26853418350219727},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20018959045410156}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8151466846466064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6780349016189575},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.5196325182914734},{"id":"https://openalex.org/C29738020","wikidata":"https://www.wikidata.org/wiki/Q217605","display_name":"Claw","level":2,"score":0.4853290617465973},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45216476917266846},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.451654314994812},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3431187868118286},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.26853418350219727},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20018959045410156},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11080417","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080417","pdf_url":"https://www.mdpi.com/2075-1680/11/8/417/pdf?version=1660891556","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6de0c8d6e50c492ea2a1a09c77aec7aa","is_oa":true,"landing_page_url":"https://doaj.org/article/6de0c8d6e50c492ea2a1a09c77aec7aa","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 8, p 417 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/8/417/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11080417","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 8; Pages: 417","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11080417","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11080417","pdf_url":"https://www.mdpi.com/2075-1680/11/8/417/pdf?version=1660891556","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4292547926.pdf","grobid_xml":"https://content.openalex.org/works/W4292547926.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1967979192","https://openalex.org/W2040576723","https://openalex.org/W2056043440","https://openalex.org/W2069905179","https://openalex.org/W2074222613","https://openalex.org/W2109431058","https://openalex.org/W2120974719","https://openalex.org/W2402119833","https://openalex.org/W4232896595","https://openalex.org/W4249665279","https://openalex.org/W4254224703"],"related_works":["https://openalex.org/W2079112245","https://openalex.org/W1989846519","https://openalex.org/W2950390960","https://openalex.org/W2079330337","https://openalex.org/W2226543729","https://openalex.org/W4303105543","https://openalex.org/W1527576459","https://openalex.org/W2531609948","https://openalex.org/W2022023572","https://openalex.org/W4311654148"],"abstract_inverted_index":{"In":[0,105],"2014,":[1],"some":[2],"scholars":[3],"showed":[4],"that":[5,117,129],"every":[6,118],"2-connected":[7,112],"claw-free":[8,113,144],"graph":[9,55],"G":[10,56,115,122],"with":[11,17,146],"independence":[12],"number":[13,97],"\u03b1(G)\u22643":[14],"is":[15,57,102],"Hamiltonian":[16],"one":[18],"exception":[19],"of":[20,22,32,38,51,53,70,72,98,121],"family":[21],"graphs.":[23],"If":[24,91],"a":[25,46,54,59,82,87,92],"nontrivial":[26],"path":[27],"contains":[28],"only":[29],"internal":[30,68],"vertices":[31,37,69],"degree":[33,39],"two":[34],"and":[35,67,127],"end":[36],"not":[40],"two,":[41],"then":[42,100],"we":[43,63,108],"call":[44],"it":[45,101],"branch.":[47],"A":[48],"set":[49],"S":[50,73],"branches":[52,71],"called":[58,103],"branch":[60,83,89,126],"cut":[61],"if":[62],"delete":[64],"all":[65,111],"edges":[66],"leading":[74],"to":[75,85],"more":[76],"components":[77],"than":[78],"G.":[79],"We":[80,135],"use":[81],"bond":[84],"denote":[86],"minimal":[88],"cut.":[90],"branch-bond":[93,120],"has":[94,123,132],"an":[95,124],"odd":[96,119],"branches,":[99],"odd.":[104],"this":[106],"paper,":[107],"shall":[109],"characterize":[110],"graphs":[114,145],"such":[116,128],"edge":[125],"\u03b1(G)\u22645":[130],"but":[131],"no":[133],"2-factor.":[134],"also":[136],"consider":[137],"the":[138],"same":[139],"problem":[140],"for":[141],"those":[142],"2-edge-connected":[143],"\u03b1(G)\u22644.":[147]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-08-22T00:00:00"}