{"id":"https://openalex.org/W3008087224","doi":"https://doi.org/10.3390/sym12020304","title":"Recognition and Optimization Algorithms for P5-Free Graphs","display_name":"Recognition and Optimization Algorithms for P5-Free Graphs","publication_year":2020,"publication_date":"2020-02-20","ids":{"openalex":"https://openalex.org/W3008087224","doi":"https://doi.org/10.3390/sym12020304","mag":"3008087224"},"language":"en","primary_location":{"id":"doi:10.3390/sym12020304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020304","pdf_url":"https://www.mdpi.com/2073-8994/12/2/304/pdf?version=1582960363","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/2/304/pdf?version=1582960363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041978796","display_name":"Mihai T\u0103lmaciu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210142575","display_name":"University of Bac\u0103u","ror":"https://ror.org/03x3axr33","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210142575"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Mihai Talmaciu","raw_affiliation_strings":["\u201cVasile Alecsandri\u201d University of Bacau, Calea Marasesti 157, 600115 Bacau, Romania","\"Vasile Alecsandri\" University of Bacau, Calea Marasesti 157, 600115 Bacau, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u201cVasile Alecsandri\u201d University of Bacau, Calea Marasesti 157, 600115 Bacau, Romania","institution_ids":["https://openalex.org/I4210142575"]},{"raw_affiliation_string":"\"Vasile Alecsandri\" University of Bacau, Calea Marasesti 157, 600115 Bacau, Romania","institution_ids":["https://openalex.org/I4210142575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067782114","display_name":"Lumini\u0163a Dumitriu","orcid":"https://orcid.org/0000-0002-7277-0747"},"institutions":[{"id":"https://openalex.org/I3122748864","display_name":"\"Dunarea de Jos\" University of Galati","ror":"https://ror.org/052sta926","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122748864"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Lumini\u0163a Dumitriu","raw_affiliation_strings":["\u201cDunarea de Jos\u201d University of Galati, Domneasca 47, 800008 Galati, Romania","\"Dunarea de Jos\" University of Galati, Domneasca 47, 800008 Galati, Romania"],"raw_orcid":"https://orcid.org/0000-0002-7277-0747","affiliations":[{"raw_affiliation_string":"\u201cDunarea de Jos\u201d University of Galati, Domneasca 47, 800008 Galati, Romania","institution_ids":["https://openalex.org/I3122748864"]},{"raw_affiliation_string":"\"Dunarea de Jos\" University of Galati, Domneasca 47, 800008 Galati, Romania","institution_ids":["https://openalex.org/I3122748864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029731309","display_name":"Ioan \u0218u\u0219nea","orcid":"https://orcid.org/0000-0003-4795-4699"},"institutions":[{"id":"https://openalex.org/I3122748864","display_name":"\"Dunarea de Jos\" University of Galati","ror":"https://ror.org/052sta926","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122748864"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ioan \u015eu\u015fnea","raw_affiliation_strings":["\u201cDunarea de Jos\u201d University of Galati, Domneasca 47, 800008 Galati, Romania","\"Dunarea de Jos\" University of Galati, Domneasca 47, 800008 Galati, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u201cDunarea de Jos\u201d University of Galati, Domneasca 47, 800008 Galati, Romania","institution_ids":["https://openalex.org/I3122748864"]},{"raw_affiliation_string":"\"Dunarea de Jos\" University of Galati, Domneasca 47, 800008 Galati, Romania","institution_ids":["https://openalex.org/I3122748864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091292514","display_name":"Victor Lepin","orcid":null},"institutions":[{"id":"https://openalex.org/I151823869","display_name":"National Academy of Sciences of Belarus","ror":"https://ror.org/02j8pe645","country_code":"BY","type":"government","lineage":["https://openalex.org/I151823869"]},{"id":"https://openalex.org/I4210105280","display_name":"Institute of Mathematics","ror":"https://ror.org/00vsg3p53","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210105280","https://openalex.org/I4210116091"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"Victor Lepin","raw_affiliation_strings":["Institute of Mathematics of National Academy of Sciences of Belarus, Surganov 11, 220072 Minsk, Belarus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of National Academy of Sciences of Belarus, Surganov 11, 220072 Minsk, Belarus","institution_ids":["https://openalex.org/I151823869","https://openalex.org/I4210105280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014955909","display_name":"L\u00e1szl\u00f3 Barna Iantovics","orcid":"https://orcid.org/0000-0001-6254-9291"},"institutions":[{"id":"https://openalex.org/I3125032317","display_name":"Universitatea de Medicin\u0103, Farmacie, \u0218tiin\u021be \u0219i Tehnologie \u201eGeorge Emil Palade\u201d din T\u00e2rgu Mure\u0219","ror":"https://ror.org/03gwbzf29","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125032317"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"L\u00e1szl\u00f3 Barna Iantovics","raw_affiliation_strings":["\u201cGeorge Emil Palade\u201d University of Medicine, Pharmacy, Sciences and Technology of Tg. Mures, Gh. Marinescu 38, 540139 Tg. Mures, Romania","\"George Emil Palade\" University of Medicine, Pharmacy, Sciences and Technology of Tg. Mures, Gh. Marinescu 38, 540139 Tg. Mures, Romania"],"raw_orcid":"https://orcid.org/0000-0001-6254-9291","affiliations":[{"raw_affiliation_string":"\u201cGeorge Emil Palade\u201d University of Medicine, Pharmacy, Sciences and Technology of Tg. Mures, Gh. Marinescu 38, 540139 Tg. Mures, Romania","institution_ids":["https://openalex.org/I3125032317"]},{"raw_affiliation_string":"\"George Emil Palade\" University of Medicine, Pharmacy, Sciences and Technology of Tg. Mures, Gh. Marinescu 38, 540139 Tg. Mures, Romania","institution_ids":["https://openalex.org/I3125032317"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5014955909","https://openalex.org/A5041978796"],"corresponding_institution_ids":["https://openalex.org/I3125032317","https://openalex.org/I4210142575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04773174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"2","first_page":"304","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9990000128746033,"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":0.9990000128746033,"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/independent-set","display_name":"Independent set","score":0.8009472489356995},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7878193259239197},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.7052587270736694},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.6426184177398682},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.622548520565033},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5802061557769775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5669462084770203},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.5666748285293579},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5092998743057251},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.48758095502853394},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.47757819294929504},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.4630890190601349},{"id":"https://openalex.org/keywords/clique-problem","display_name":"Clique problem","score":0.4534454941749573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4343448579311371},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.41141268610954285},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3688167929649353},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.16616353392601013}],"concepts":[{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.8009472489356995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7878193259239197},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.7052587270736694},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.6426184177398682},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.622548520565033},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5802061557769775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5669462084770203},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.5666748285293579},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5092998743057251},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.48758095502853394},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.47757819294929504},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.4630890190601349},{"id":"https://openalex.org/C150997102","wikidata":"https://www.wikidata.org/wiki/Q1196873","display_name":"Clique problem","level":5,"score":0.4534454941749573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4343448579311371},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.41141268610954285},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3688167929649353},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.16616353392601013}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12020304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020304","pdf_url":"https://www.mdpi.com/2073-8994/12/2/304/pdf?version=1582960363","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6dbcf3947d7f4f409e4591c671390c24","is_oa":true,"landing_page_url":"https://doaj.org/article/6dbcf3947d7f4f409e4591c671390c24","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 2, p 304 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/2/304/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12020304","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12020304","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020304","pdf_url":"https://www.mdpi.com/2073-8994/12/2/304/pdf?version=1582960363","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1736212236","https://openalex.org/W1882281809","https://openalex.org/W1957689366","https://openalex.org/W1985038305","https://openalex.org/W2003292013","https://openalex.org/W2009419163","https://openalex.org/W2071801594","https://openalex.org/W2122160710","https://openalex.org/W2150704108","https://openalex.org/W2240276843","https://openalex.org/W2282776087","https://openalex.org/W2345980508","https://openalex.org/W2486237862","https://openalex.org/W2766128142","https://openalex.org/W2768194368","https://openalex.org/W2783466236","https://openalex.org/W2835349798","https://openalex.org/W2913398500","https://openalex.org/W2938839021","https://openalex.org/W2964258819","https://openalex.org/W2981729031","https://openalex.org/W4297693688","https://openalex.org/W6678521656","https://openalex.org/W6690026968","https://openalex.org/W6742669324"],"related_works":["https://openalex.org/W3003449463","https://openalex.org/W2963989216","https://openalex.org/W2088153883","https://openalex.org/W2051627428","https://openalex.org/W2046263886","https://openalex.org/W77483341","https://openalex.org/W2078489643","https://openalex.org/W2004663694","https://openalex.org/W2045135589","https://openalex.org/W4300330793"],"abstract_inverted_index":{"The":[0,20,51,81],"weighted":[1],"independent":[2,56,92,154],"set":[3,59,93],"problem":[4],"on":[5],"P":[6,23,47,64,100],"5":[7,24,48,65,101],"-free":[8,25,49,66,102],"graphs":[9,26,103],"has":[10],"numerous":[11],"applications,":[12],"including":[13],"data":[14],"mining":[15],"and":[16,38,85,90,115,138,158,175],"dispatching":[17],"in":[18,29,43,74,143,160],"railways.":[19],"recognition":[21,129],"of":[22,46,53,151,170],"is":[27,94,111],"executed":[28],"polynomial":[30],"time.":[31,80],"Many":[32],"problems,":[33,83],"such":[34],"as":[35,110],"chromatic":[36,140],"number":[37,137,169,174],"dominating":[39,113,173],"set,":[40],"are":[41,88,108,117],"NP-hard":[42],"the":[44,91,99,105,112,135,139,149,168,172,176],"class":[45],"graphs.":[50],"size":[52,150],"a":[54,63,152],"minimum":[55,153,177],"feedback":[57,155],"vertex":[58,156],"that":[60],"belongs":[61],"to":[62],"graph":[67],"with":[68],"n":[69,77,122,124,146,163],"vertices":[70],"can":[71],"be":[72],"computed":[73],"O":[75,120,144,161],"(":[76,121,123,145,162],"16":[78],")":[79,127,128,147,166],"unweighted":[82],"clique":[84,86,136,178],"cover,":[87],"NP-complete":[89],"polynomial.":[95],"In":[96],"this":[97],"work,":[98],"using":[104],"weak":[106],"decomposition":[107],"characterized,":[109],"clique,":[114],"they":[116],"given":[118],"an":[119],"+":[125,164],"m":[126,165],"algorithm.":[130],"Additionally,":[131],"we":[132],"calculate":[133],"directly":[134],"number;":[141],"determine":[142,159],"time,":[148],"set;":[157],"time":[167],"stability,":[171],"cover.":[179]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-03-06T00:00:00"}