{"id":"https://openalex.org/W2072710027","doi":"https://doi.org/10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","title":"Recognizing triangle-free graphs with induced path-cycle double covers is NP-complete","display_name":"Recognizing triangle-free graphs with induced path-cycle double covers is NP-complete","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2072710027","doi":"https://doi.org/10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","mag":"2072710027"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5060263835","display_name":"Michael S. Jacobson","orcid":"https://orcid.org/0000-0003-2220-8622"},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael S. Jacobson","raw_affiliation_strings":["Department of Mathematics, University of Louisville, Louisville, Kentucky 40292","Department of Mathematics; University of Louisville; Louisville Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Department of Mathematics; University of Louisville; Louisville Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111813939","display_name":"Andr\ufffd E. K\ufffdzdy","orcid":null},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andr\ufffd E. K\ufffdzdy","raw_affiliation_strings":["Department of Mathematics; University of Louisville; Louisville Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics; University of Louisville; Louisville Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111860776","display_name":"Jen Lehel","orcid":null},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jen? Lehel","raw_affiliation_strings":["Department of Mathematics, University of Louisville, Louisville, Kentucky 40292","Department of Mathematics; University of Louisville; Louisville Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Department of Mathematics; University of Louisville; Louisville Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060263835"],"corresponding_institution_ids":["https://openalex.org/I142740786"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.5275,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68926503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"31","issue":"1","first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9948999881744385,"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":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8390102386474609},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7595052719116211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6647834777832031},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5461198091506958},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46315377950668335},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.43587926030158997},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42465734481811523}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8390102386474609},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7595052719116211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6647834777832031},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5461198091506958},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46315377950668335},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.43587926030158997},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42465734481811523}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199801)31:1<1::aid-net1>3.0.co;2-n","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W1630514295","https://openalex.org/W1537073411","https://openalex.org/W1998397199","https://openalex.org/W2068040398","https://openalex.org/W2949537674","https://openalex.org/W3021108537","https://openalex.org/W2905396358"],"abstract_inverted_index":{"An":[0],"induced":[1,20],"path-cycle":[2],"double":[3],"cover":[4],"(IPCDC)":[5],"of":[6,19,24,50,56,62,68,98,139,154,158],"a":[7,12,39,99,131,140],"simple":[8,79,133],"graph":[9,97,108,134,138],"G":[10,25,51,63],"is":[11,38,84,106,135,161],"family":[13],"\u2131":[14],"=":[15,103],"{F1,":[16],"\u2026,":[17],"Fk}":[18],"paths":[21],"and":[22,59,120,144],"cycles":[23],"such":[26],"that":[27,76,130],"if":[28,119,122,143,146],"Fi":[29,35],"\u2229":[30,36],"Fj":[31,37],"\u2260":[32,46],"\u2298,":[33],"then":[34],"vertex":[40,61,110],"or":[41],"an":[42,82,93,149],"edge,":[43],"for":[44],"i":[45],"j,":[47],"each":[48,60],"edge":[49],"appears":[52,64],"in":[53,65,113],"precisely":[54,66],"two":[55,115,126],"the":[57,69,88,107,136,152],"Fi's,":[58],"three":[67],"Fi's.":[70],"In":[71],"this":[72],"paper,":[73],"we":[74],"prove":[75],"recognizing":[77,155],"triangle-free":[78,132],"graphs":[80,157],"with":[81,109],"IPCDC":[83],"NP-complete":[85],"by":[86],"reducing":[87],"3-Satisfiability":[89],"problem":[90,153],"to":[91],"finding":[92],"IPCDC.":[94,150],"The":[95],"dependency":[96,137,156],"3-uniform":[100,141,159],"hypergraph":[101,142],"H":[102],"(V,":[104],"E)":[105],"set":[111],"E":[112],"which":[114],"hyperedges":[116],"are":[117],"joined":[118],"only":[121,145],"they":[123],"share":[124],"exactly":[125],"elements.":[127],"We":[128],"show":[129],"it":[147],"has":[148],"Consequently,":[151],"hypergraphs":[160],"NP-complete.":[162],"\u00a9":[163],"1998":[164,173],"John":[165],"Wiley":[166],"&":[167],"Sons,":[168],"Inc.":[169],"Networks":[170],"31:":[171],"1\u201310,":[172]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}