{"id":"https://openalex.org/W2990898510","doi":"https://doi.org/10.1051/ro/2019111","title":"Remarks on path factors in graphs","display_name":"Remarks on path factors in graphs","publication_year":2019,"publication_date":"2019-11-22","ids":{"openalex":"https://openalex.org/W2990898510","doi":"https://doi.org/10.1051/ro/2019111","mag":"2990898510"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2019111","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019111","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"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"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"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":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":"Sizhong Zhou","raw_affiliation_strings":["School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, 212003 Zhenjiang, Jiangsu, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, 212003 Zhenjiang, Jiangsu, P.R. China","institution_ids":["https://openalex.org/I4210096899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101764220"],"corresponding_institution_ids":["https://openalex.org/I4210096899"],"apc_list":null,"apc_paid":null,"fwci":6.2666,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.96926381,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"54","issue":"6","first_page":"1827","last_page":"1834"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9970999956130981,"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":0.993399977684021,"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":0.8433587551116943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5637858510017395},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5469123125076294},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.47107118368148804},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.4559607207775116},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4551841914653778},{"id":"https://openalex.org/keywords/path-graph","display_name":"Path graph","score":0.4383728504180908},{"id":"https://openalex.org/keywords/factor-critical-graph","display_name":"Factor-critical graph","score":0.42867082357406616},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.29103103280067444}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8433587551116943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5637858510017395},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5469123125076294},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.47107118368148804},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.4559607207775116},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4551841914653778},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.4383728504180908},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.42867082357406616},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.29103103280067444}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2019111","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019111","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"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"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2020__54_6_1827_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2019111/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1432702782","https://openalex.org/W1963596676","https://openalex.org/W2005371816","https://openalex.org/W2008496735","https://openalex.org/W2012966668","https://openalex.org/W2030294818","https://openalex.org/W2037953913","https://openalex.org/W2054195094","https://openalex.org/W2072174759","https://openalex.org/W2086829022","https://openalex.org/W2119433758","https://openalex.org/W2122666717","https://openalex.org/W2135972039","https://openalex.org/W2140329547","https://openalex.org/W2512607386","https://openalex.org/W2556378519","https://openalex.org/W2560327106","https://openalex.org/W2569203870","https://openalex.org/W2607117956","https://openalex.org/W2619803636","https://openalex.org/W2802019301","https://openalex.org/W2890163737","https://openalex.org/W2945604472","https://openalex.org/W4233263631"],"related_works":["https://openalex.org/W2226543729","https://openalex.org/W3157164550","https://openalex.org/W2404212820","https://openalex.org/W2077631478","https://openalex.org/W4288436438","https://openalex.org/W4242930043","https://openalex.org/W4298388358","https://openalex.org/W1970462054","https://openalex.org/W4229970255","https://openalex.org/W4291556361"],"abstract_inverted_index":{"A":[0,20,37,80],"spanning":[1],"subgraph":[2],"of":[3,12,102,107],"a":[4,9,26,43,59,86,110,122,154],"graph":[5,14,38,52,81,95,106,123,155],"is":[6,40,83,125,157],"defined":[7,41,84],"as":[8,42,85],"path":[10,27],"factor":[11,28],"the":[13,104],"if":[15,53,96,133,165],"its":[16],"component":[17,31],"are":[18],"paths.":[19],"P":[21,45,60,88,111,127,159],"\u2265":[22,46,61,89,112,138,148,170,179],"n":[23,35,47,62,90,113],"-factor":[24,63],"means":[25],"with":[29,73],"each":[30],"having":[32],"at":[33],"least":[34],"vertices.":[36],"G":[39,54,71,82,103,108,124,136,146,156,168,177],"(":[44,70,87,126,135,145,158,167,176],",":[48,91,129,161],"m":[49,78,130,140],")-factor":[50,93,131,163],"deleted":[51,132],"\u2013":[55],"E":[56,66,69,75],"\u2032":[57,67],"has":[58],"for":[64],"every":[65],"\u2286":[68],")":[72,137,147,169,178],"|":[74],"\u2032|":[76],"=":[77],".":[79],"k":[92,100,162,171],"critical":[94,164],"after":[97],"deleting":[98],"any":[99],"vertices":[101],"remaining":[105],"admits":[109],"-factor.":[114],"In":[115],"this":[116],"paper,":[117],"we":[118],"demonstrate":[119],"that":[120],"(i)":[121],"\u22653":[128,160],"\u03ba":[134,166],"2":[139,173],"+":[141,172],"1":[142],"and":[143,174],"bind":[144,175],"2/3":[149],"-":[150],"$":[151,180],"\\frac{3}{2}-\\frac{1}{4m+4}$;":[152],"(ii)":[153],"\\frac{5+k}{4}$.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":9}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}