{"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/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"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":false,"raw_author_name":"Sizhong Zhou","raw_affiliation_strings":["School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China"],"raw_orcid":null,"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"],"raw_orcid":null,"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":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04193721,"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/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"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/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393031595.pdf","grobid_xml":"https://content.openalex.org/works/W4393031595.grobid-xml"},"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":[0,31,48,69],"spanning":[1],"subgraph":[2],"F":[3,15],"of":[4,14,19,33],"G":[5,34,50,63,71,91,102,127,149,166,183],"is":[6,16,51,72,94,103,150,167,184],"called":[7,52,73],"a":[8,17,36,53,65,74,95,133],"path":[9,18,37],"factor":[10,38],"if":[11,57,80,108,155,172,189],"every":[12,41],"component":[13,42],"order":[20],"at":[21,44],"least":[22,45],"2.":[23],"Let":[24],"k":[25,46],"\u2265":[26],"2":[27],"be":[28],"an":[29,142,159,176],"integer.":[30],"P\u2265k-factor":[32,54,66,96],"means":[35],"in":[39],"which":[40],"has":[43,64],"vertices.":[47],"graph":[49,56,70,79,148,165,182],"avoidable":[55,78,97,107,154,171,188],"for":[58,81,109],"any":[59,82,110,120],"e":[60,121,131],"\u2208":[61,122],"E(G),":[62],"avoiding":[67],"e.":[68],"(P\u2265k,":[75,104],"n)-factor":[76,105,152,169,186],"critical":[77,106,153,170,187],"W":[83,93,111,125,129],"\u2286":[84,112],"V":[85,113],"(G)":[86,114],"with":[87,115],"|W|":[88,116],"=":[89,117],"n,":[90],"\u2212":[92,124,128,130],"graph.":[98],"In":[99,135],"other":[100],"words,":[101],"n":[118,193],"and":[119,194],"E(G":[123],"),":[126],"admits":[132],"P\u2265k-factor.":[134],"this":[136],"article,":[137],"we":[138],"verify":[139],"that":[140],"(i)":[141],"(n":[143,160,177],"+":[144,146,161,163,178,180],"r":[145,162,179,195],"2)-connected":[147,164,181],"(P\u22652,":[151],"I(G)>(n+r+2)/(2(r+2))":[156],";":[157,174,191],"(ii)":[158],"(P\u22653,":[168,185],"t(G)>(n+r+2)/(2(r+2))":[173],"(iii)":[175],"I(G)>(n+3(r+2))/(2(r+2))":[190],"where":[192],"are":[196],"two":[197],"nonnegative":[198],"integers.":[199]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
