{"id":"https://openalex.org/W4393031595","doi":"https://doi.org/10.1051/ro/2024071","title":"Some existence theorems on path-factor critical avoidable graphs","display_name":"Some existence theorems on path-factor critical avoidable graphs","publication_year":2024,"publication_date":"2024-03-01","ids":{"openalex":"https://openalex.org/W4393031595","doi":"https://doi.org/10.1051/ro/2024071"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024071","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024071","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/02/ro230771.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/02/ro230771.pdf","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":"Sizhong Zhou","raw_affiliation_strings":["School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China","institution_ids":["https://openalex.org/I4210096899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100434452","display_name":"Hongxia Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I18452120","display_name":"Yantai University","ror":"https://ror.org/01rp41m56","country_code":"CN","type":"education","lineage":["https://openalex.org/I18452120"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongxia Liu","raw_affiliation_strings":["School of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, P.R. China","institution_ids":["https://openalex.org/I18452120"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101764220"],"corresponding_institution_ids":["https://openalex.org/I4210096899"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04581388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"2","first_page":"2015","last_page":"2027"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9926000237464905,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9714999794960022,"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/factor","display_name":"Factor (programming language)","score":0.6438223719596863},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6366326808929443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.534852147102356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37390977144241333},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32796967029571533},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3209437131881714},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06820383667945862}],"concepts":[{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.6438223719596863},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6366326808929443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.534852147102356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37390977144241333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32796967029571533},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3209437131881714},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06820383667945862}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2024071","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024071","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/02/ro230771.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2024071","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024071","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/02/ro230771.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393031595.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1963596676","https://openalex.org/W1975099798","https://openalex.org/W1988845443","https://openalex.org/W1989046128","https://openalex.org/W2034647200","https://openalex.org/W2037953913","https://openalex.org/W2072174759","https://openalex.org/W2074508519","https://openalex.org/W2113050592","https://openalex.org/W2122666717","https://openalex.org/W2560327106","https://openalex.org/W2895001549","https://openalex.org/W2944187207","https://openalex.org/W2963781957","https://openalex.org/W3092050107","https://openalex.org/W3108558482","https://openalex.org/W3159544998","https://openalex.org/W3168478447","https://openalex.org/W3208979361","https://openalex.org/W4291163881","https://openalex.org/W4310153179","https://openalex.org/W4313593837","https://openalex.org/W4322623894","https://openalex.org/W4366400921","https://openalex.org/W4385369253","https://openalex.org/W4388168755","https://openalex.org/W4391979668","https://openalex.org/W4392154240","https://openalex.org/W4395091195"],"related_works":["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/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W2963966623"],"abstract_inverted_index":{"A":[0,31,51,82],"spanning":[1],"subgraph":[2],"F":[3,15],"of":[4,14,19,36],"G":[5,37,53,70,72,84,105,112,126,144,156,160,186,199,217,230,248,261],"is":[6,16,54,85,115,127,187,218,249],"called":[7,55,86],"a":[8,17,39,56,74,87,116,166],"path":[9,18,40],"factor":[10,41],"if":[11,63,98,137,196,227,258],"every":[12,44],"component":[13,45],"order":[20],"at":[21,47],"least":[22,48],"2.":[23],"Let":[24],"k":[25,34,49,59,77,91,119,131,169],"\u2265":[26,33,58,76,90,118,130,168],"2":[27],"be":[28],"an":[29,178,209,240],"integer.":[30],"P":[32,57,75,89,117,129,167,189,220,251],"-factor":[35,60,78,120],"means":[38],"in":[42],"which":[43],"has":[46,73],"vertices.":[50],"graph":[52,62,83,97,185,216,247],"avoidable":[61,96,121,136,195,226,257],"for":[64,99,138],"any":[65,100,139,151],"e":[66,80,152,164],"\u2208":[67,153],"E":[68,154],"(":[69,88,104,128,143,155,179,188,198,210,219,229,241,250,260],"),":[71,159],"avoiding":[79],".":[81],",":[92,111,132,191,222,253],"n":[93,110,133,149,180,192,201,211,223,232,242,254,263,271],")-factor":[94,134,193,224,255],"critical":[95,135,194,225,256],"W":[101,114,140,158,162],"\u2286":[102,141],"V":[103,142],")":[106,145],"with":[107,146],"|W|":[108,147],"=":[109,148],"\u2212":[113,157,161,163],"graph.":[122],"In":[123,171],"other":[124],"words,":[125],"and":[150,272],"admits":[165],"-factor.":[170],"this":[172],"article,":[173],"we":[174],"verify":[175],"that":[176],"(i)":[177],"+":[181,183,202,212,214,233,243,245],"r":[182,203,205,213,234,236,244,265,267,273],"2)-connected":[184,215,246],"\u22652":[190],"I":[197,259],")>(":[200,231,262],"+2)/(2(":[204,235],"+2))":[206,237,268],";":[207,238,269],"(ii)":[208],"\u22653":[221,252],"t":[228],"(iii)":[239],"+3(":[264],"+2))/(2(":[266],"where":[270],"are":[274],"two":[275],"nonnegative":[276],"integers.":[277]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}