{"id":"https://openalex.org/W4296838213","doi":"https://doi.org/10.7151/dmgt.2471","title":"A \\sigma3 condition for arbitrarily partitionable graphs","display_name":"A \\sigma3 condition for arbitrarily partitionable graphs","publication_year":2022,"publication_date":"2022-09-23","ids":{"openalex":"https://openalex.org/W4296838213","doi":"https://doi.org/10.7151/dmgt.2471"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.7151/dmgt.2471","pdf_url":"https://www.dmgt.uz.zgora.pl/publish/pdf.php?doi=2471","source":{"id":"https://openalex.org/S2738357781","display_name":"Discussiones Mathematicae Graph Theory","issn_l":"1234-3099","issn":["1234-3099","2083-5892"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.dmgt.uz.zgora.pl/publish/pdf.php?doi=2471","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032196380","display_name":"Julien Bensmail","orcid":"https://orcid.org/0000-0002-9292-394X"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Julien Bensmail","raw_affiliation_strings":["Combinatorics, Optimization and Algorithms for Telecommunications"],"affiliations":[{"raw_affiliation_string":"Combinatorics, Optimization and Algorithms for Telecommunications","institution_ids":["https://openalex.org/I4210099593"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032196380"],"corresponding_institution_ids":["https://openalex.org/I4210099593"],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":0.203,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":1,"citation_normalized_percentile":{"value":0.412021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":60,"max":71},"biblio":{"volume":"44","issue":"2","first_page":"755","last_page":"755"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998,"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":0.9998,"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":0.9996,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9989,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/sigma","display_name":"Sigma","score":0.63758516}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8884703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7585162},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.63758516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4231826},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.7151/dmgt.2471","pdf_url":"https://www.dmgt.uz.zgora.pl/publish/pdf.php?doi=2471","source":{"id":"https://openalex.org/S2738357781","display_name":"Discussiones Mathematicae Graph Theory","issn_l":"1234-3099","issn":["1234-3099","2083-5892"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://hal.science/hal-03665116","pdf_url":"https://hal.science/hal-03665116/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.science/hal-03665116v2/file/sigma3ap.pdf","pdf_url":"https://hal.science/hal-03665116v2/file/sigma3ap.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.science/hal-03665116v2/document","pdf_url":"https://hal.science/hal-03665116v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.7151/dmgt.2471","pdf_url":"https://www.dmgt.uz.zgora.pl/publish/pdf.php?doi=2471","source":{"id":"https://openalex.org/S2738357781","display_name":"Discussiones Mathematicae Graph Theory","issn_l":"1234-3099","issn":["1234-3099","2083-5892"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.41,"display_name":"Reduced inequalities"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":14,"referenced_works":["https://openalex.org/W1966882057","https://openalex.org/W2035089435","https://openalex.org/W2036486897","https://openalex.org/W2047452025","https://openalex.org/W2053543588","https://openalex.org/W2135700202","https://openalex.org/W2178768069","https://openalex.org/W2569808087","https://openalex.org/W2576200721","https://openalex.org/W2900173647","https://openalex.org/W3116237911","https://openalex.org/W4233756358","https://openalex.org/W4393902337","https://openalex.org/W825559216"],"related_works":["https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W3002753104","https://openalex.org/W2911598644","https://openalex.org/W2077600819","https://openalex.org/W2061531152","https://openalex.org/W2042127053","https://openalex.org/W2007980826","https://openalex.org/W1979597421","https://openalex.org/W1587224694"],"abstract_inverted_index":{"A":[0],"graph":[1,33,66,120,159],"G":[2,160,167,201,208,212,222],"of":[3,25,34,48,80,133,141,150,161],"order":[4,35,162],"n":[5,163,194,219],"is":[6,28,71,85,127,164,168,196,209,213],"arbitrarily":[7],"partitionable":[8],"(AP":[9],"for":[10,13,38,94,108,117,135,200],"short)":[11],"if,":[12],"every":[14,39],"partition":[15],"(\u03bb":[16],"1":[17],",":[18,115],".":[19,20,43,44],".,":[21,45],"\u03bb":[22,36],"p":[23],")":[24],"n,":[26,175],"there":[27],"a":[29,31,78,105,118,136,198,224],"partitionis":[30],"connected":[32],"i":[37,40],"\u2208":[41],"{1,":[42],"p}.Several":[46],"aspects":[47],"AP":[49,83,210],"graphs":[50,61,84,95],"have":[51],"been":[52],"investigated":[53],"to":[54,59,74,89,96,202],"date,":[55],"including":[56],"their":[57],"connection":[58],"Hamiltonian":[60,69,98],"and":[62,77,148,154,170,176,221],"traceable":[63,65,177],"graphs.Every":[64],"(and,":[67],"thus,":[68],"graph)":[70],"indeed":[72],"known":[73,91],"be":[75,97,203],"AP,":[76],"line":[79],"research":[81],"on":[82],"thus":[86],"about":[87],"weakening,":[88],"APness,":[90],"sufficient":[92,106],"conditions":[93],"or":[99,227],"traceable.In":[100],"this":[101],"work,":[102],"we":[103,184,205],"provide":[104],"condition":[107],"APness":[109],"involving":[110],"the":[111,122,130],"parameter":[112,123],"\u03c3":[113,124,171,179,190,215],"3":[114,125,172,180,191,216],"where,":[116],"given":[119],"G,":[121],"(G)":[126,173,181,192,217],"defined":[128],"as":[129],"minimum":[131],"value":[132],"d(u)|":[134],"set":[137],"{u,":[138],"v,":[139,147],"w}":[140],"three":[142],"pairwise":[143],"independent":[144],"vertices":[145],"u,":[146],"w":[149],"G.":[151],"Flandrin,":[152],"Jung,":[153],"Li":[155],"proved":[156],"that":[157,188,207],"any":[158],"Hamitonian":[165],"provided":[166,178,211],"2-connected":[169],"\u2265":[174,182,193,218],"n-1.Unfortunately,":[183],"exhibit":[185],"examples":[186],"showing":[187],"having":[189],"-2":[195],"not":[197],"guarantee":[199],"AP.However,":[204],"prove":[206],"2-connected,":[214],"-2,":[220],"has":[223],"perfect":[225],"matching":[226],"quasi-perfect":[228],"matching.":[229]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4296838213","counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2024-12-08T05:21:40.372742","created_date":"2022-09-24"}