{"id":"https://openalex.org/W3124981905","doi":"https://doi.org/10.1134/s0032946020040043","title":"A Sufficient Condition for the Existence of Restricted Fractional (g,\u00a0f)-Factors in Graphs","display_name":"A Sufficient Condition for the Existence of Restricted Fractional (g,\u00a0f)-Factors in Graphs","publication_year":2020,"publication_date":"2020-12-01","ids":{"openalex":"https://openalex.org/W3124981905","doi":"https://doi.org/10.1134/s0032946020040043","mag":"3124981905"},"language":"en","primary_location":{"id":"doi:10.1134/s0032946020040043","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946020040043","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","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/A5101764220","display_name":"Sizhong Zhou","orcid":"https://orcid.org/0000-0003-2093-2158"},"institutions":[{"id":"https://openalex.org/I4210096899","display_name":"Jiangsu University of Science and Technology","ror":"https://ror.org/00tyjp878","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210096899"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"S. Zhou","raw_affiliation_strings":["School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China","institution_ids":["https://openalex.org/I4210096899"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Z. Sun","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Sun","raw_affiliation_strings":["School of Mathematical Sciences, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044205491","display_name":"Quanru Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096899","display_name":"Jiangsu University of Science and Technology","ror":"https://ror.org/00tyjp878","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210096899"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Q. Pan","raw_affiliation_strings":["School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China","institution_ids":["https://openalex.org/I4210096899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101764220"],"corresponding_institution_ids":["https://openalex.org/I4210096899"],"apc_list":null,"apc_paid":null,"fwci":2.3314,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.91163441,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"4","first_page":"332","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9969000220298767,"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":0.9882000088691711,"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/combinatorics","display_name":"Combinatorics","score":0.6955685019493103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6841492056846619},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.602451741695404},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5736292004585266},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41399022936820984},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3857128918170929}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6955685019493103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6841492056846619},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.602451741695404},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5736292004585266},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41399022936820984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3857128918170929},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0032946020040043","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946020040043","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1980838889","https://openalex.org/W1986600094","https://openalex.org/W2007435743","https://openalex.org/W2008496735","https://openalex.org/W2068431006","https://openalex.org/W2098246804","https://openalex.org/W2351151637","https://openalex.org/W2394588990","https://openalex.org/W2569203870","https://openalex.org/W2611093227","https://openalex.org/W2619803636","https://openalex.org/W2779427255","https://openalex.org/W2783432306","https://openalex.org/W2887844622","https://openalex.org/W2890163737","https://openalex.org/W2900236623","https://openalex.org/W2944187207","https://openalex.org/W2945604472","https://openalex.org/W2946451706","https://openalex.org/W2963667431","https://openalex.org/W2964824910","https://openalex.org/W2984793906","https://openalex.org/W2990898510","https://openalex.org/W2997092311","https://openalex.org/W2999068088","https://openalex.org/W2999554972","https://openalex.org/W3008761226","https://openalex.org/W3196602131","https://openalex.org/W4232896595"],"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/W4288278856","https://openalex.org/W2572370460","https://openalex.org/W3111310291"],"abstract_inverted_index":{"In":[0,203],"an":[1,188],"NFV":[2,22,41,189,213],"network,":[3],"the":[4,13,16,20,27,40,185,208,244,248,253,257],"availability":[5],"of":[6,15,29,46,80,127,172,187,201],"resource":[7,209],"scheduling":[8,210],"can":[9,36],"be":[10,54],"transformed":[11],"to":[12,38,117,178,184,227,234],"existence":[14,28],"fractional":[17,31,77,119,148,180,236],"factor":[18],"in":[19,33,198,212,252,260],"corresponding":[21],"network":[23,34,42,190],"graph.":[24],"Researching":[25],"on":[26,247],"special":[30],"factors":[32],"structure":[35,186],"help":[37],"construct":[39],"with":[43,68,82,115,133,152,176,232],"efficient":[44],"application":[45],"resources.":[47],"Let":[48],"h:":[49],"E(G)":[50],"\u2192":[51],"[0,":[52],"1]":[53],"a":[55,65,76,118,147,179,220,225,235],"function.":[56],"We":[57,63,107],"write":[58],"$${d}_{G}^{h}(x)=\\sum":[59],"\\limits_{e\\ni":[60],"x}h(e)$$":[61],".":[62],"call":[64],"graph":[66,216,226],"Fh":[67,151],"vertex":[69],"set":[70,74],"V(G)":[71],"and":[72,131,140,161,218],"edge":[73],"Eh":[75,97],"(g,":[78,120,149,181,237],"f)-factor":[79,121,150,182],"G":[81,110,145],"indicator":[83],"function":[84],"h":[85],"if":[86,122],"$$g(x)\\le":[87],"{d}_{G}^{h}(x)\\le":[88],"f(x)$$":[89],"holds":[90],"for":[91,123,156,165,224],"any":[92,124,157,166],"x":[93],"\u2208":[94,102,159,168],"V(G),":[95],"where":[96,191],"=":[98,135,138,154,163],"{e":[99],":":[100],"e":[101,158,167],"E(G),":[103],"h(e)":[104,153,162],">":[105],"0}.":[106],"say":[108],"that":[109,243],"has":[111],"property":[112,173,229],"E(m,":[113,174],"n)":[114,175,231],"respect":[116,177,233],"two":[125],"sets":[126],"independent":[128],"edges":[129],"M":[130,160],"N":[132],"\u2223M\u2223":[134],"m,":[136],"\u2223N\u2223":[137],"n,":[139],"$$M\\cap":[141],"N=\\varnothing":[142],"$$":[143],",":[144],"admits":[146],"1":[155],"0":[164],"N.":[169],"The":[170],"concept":[171],"corresponds":[183],"certain":[192],"channels":[193],"are":[194],"occupied":[195],"or":[196],"damaged":[197],"some":[199,261],"period":[200],"time.":[202],"this":[204],"paper,":[205],"we":[206],"consider":[207],"problem":[211],"networks":[214],"using":[215],"theory,":[217],"show":[219],"neighborhood":[221,249],"union":[222,250],"condition":[223,251],"have":[228],"E(1,":[230],"f)-factor.":[238],"Furthermore,":[239],"it":[240],"is":[241,256],"shown":[242],"lower":[245],"bound":[246],"main":[254],"result":[255],"best":[258],"possible":[259],"sense.":[262]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}