{"id":"https://openalex.org/W4386782072","doi":"https://doi.org/10.1051/ro/2023149","title":"On two variants of split graphs: 2-unipolar graph and k-probe-split graph","display_name":"On two variants of split graphs: 2-unipolar graph and k-probe-split graph","publication_year":2023,"publication_date":"2023-09-15","ids":{"openalex":"https://openalex.org/W4386782072","doi":"https://doi.org/10.1051/ro/2023149"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2023149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023149","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro220759.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":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","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":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro220759.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034401895","display_name":"Luciano N. Grippo","orcid":"https://orcid.org/0000-0002-0438-0595"},"institutions":[{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Luciano N. Grippo","raw_affiliation_strings":["CONICET and Universidad Nacional de General Sarmiento, Los Polvorines, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CONICET and Universidad Nacional de General Sarmiento, Los Polvorines, Argentina","institution_ids":["https://openalex.org/I35953669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071911310","display_name":"Ver\u00f3nica Moyano","orcid":"https://orcid.org/0000-0002-6954-4992"},"institutions":[{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Ver\u00f3nica A. Moyano","raw_affiliation_strings":["CONICET and Universidad Nacional de General Sarmiento, Los Polvorines, Argentina"],"raw_orcid":"https://orcid.org/0000-0002-6954-4992","affiliations":[{"raw_affiliation_string":"CONICET and Universidad Nacional de General Sarmiento, Los Polvorines, Argentina","institution_ids":["https://openalex.org/I35953669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071911310"],"corresponding_institution_ids":["https://openalex.org/I35953669"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":{"value":0,"currency":"USD","value_usd":0},"fwci":0.1396,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4908534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"58","issue":"4","first_page":"3597","last_page":"3606"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5728609561920166},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49965691566467285},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.42102310061454773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41385048627853394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35200098156929016}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5728609561920166},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49965691566467285},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.42102310061454773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41385048627853394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35200098156929016}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2023149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023149","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro220759.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":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","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/2023149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023149","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro220759.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":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","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":[{"id":"https://openalex.org/G3897044667","display_name":null,"funder_award_id":"PIP 2022-2024-GI","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G4721439447","display_name":null,"funder_award_id":"PIP2022","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G8375604969","display_name":null,"funder_award_id":"PIP 2022-2024 GI - 11220210100392CO","funder_id":"https://openalex.org/F8784648983","funder_display_name":"Universidad Nacional de General Sarmiento"},{"id":"https://openalex.org/G953310655","display_name":null,"funder_award_id":"PIP2022-2024","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"}],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F8784648983","display_name":"Universidad Nacional de General Sarmiento","ror":"https://ror.org/01k6h2m87"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386782072.pdf","grobid_xml":"https://content.openalex.org/works/W4386782072.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W65951963","https://openalex.org/W803458648","https://openalex.org/W1970348285","https://openalex.org/W2003128536","https://openalex.org/W2007560929","https://openalex.org/W2028775537","https://openalex.org/W2051576576","https://openalex.org/W2058202744","https://openalex.org/W2064721098","https://openalex.org/W2075497674","https://openalex.org/W2113596268","https://openalex.org/W2116453796","https://openalex.org/W2179342000","https://openalex.org/W2562739206","https://openalex.org/W2606500388","https://openalex.org/W2748096547","https://openalex.org/W2903764142","https://openalex.org/W2914970624","https://openalex.org/W2950324051"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","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/W2362020254"],"abstract_inverted_index":{"A":[0,29,44,64],"graph":[1,30,54,66,70,124,130,178,187,217,229],"is":[2,32,50,57,67,75,80,132,189,201,208,226,235,248],"called":[3],"split":[4,27,205],"if":[5,34,191],"its":[6,35],"vertex":[7,36],"set":[8,15,37,152],"can":[9,38,109,171],"be":[10,39,110,122,172],"partitioned":[11,40],"into":[12,41],"a":[13,17,51,58,68,76,94,123,129,151,186,216,220,227,238],"stable":[14],"and":[16,45,55,78,198,219],"clique.":[18],"In":[19,103],"this":[20],"article,":[21],"we":[22,105],"studied":[23],"two":[24,42,90],"variants":[25],"of":[26,61,84,115,117,128,154,156,204],"graphs.":[28,63,102],"G":[31,71,121,131,188,200,218,225],"polar":[33,69],"sets":[43,144],"B":[46],"such":[47,72,138,149],"that":[48,73,107,139,150,175,185,213],"G[A]":[49,74],"complete":[52,62,85],"multipartite":[53],"G[B]":[56,79],"disjoint":[59,82],"union":[60,83],"2-unipolar":[65,101],"clique":[77],"the":[81,126,133,176,202],"graphs":[86,206],"with":[87,164],"at":[88,195],"most":[89,196],"vertices.":[91],"We":[92,183,211],"present":[93],"minimal":[95,241],"forbidden":[96,242],"induced":[97,243],"subgraph":[98],"characterization":[99,239],"for":[100,230,245],"addition,":[104],"show":[106],"they":[108],"represented":[111],"as":[112],"an":[113],"intersection":[114],"substars":[116],"special":[118],"cacti.":[119],"Let":[120],"class,":[125],"G-width":[127,194],"minimum":[134],"positive":[135,221],"integer":[136,222],"k":[137,142,197,234],"there":[140],"exist":[141],"independent":[143],"N1,":[145],"\u2026":[146,168],",":[147,169],"Nk":[148],"F":[153],"nonedges":[155],"G,":[157],"whose":[158],"endpoints":[159],"belong":[160],"to":[161,181],"some":[162,231],"Ni":[163],"i":[165],"=":[166],"1,":[167],"k,":[170,223],"added":[173],"so":[174],"resulting":[177],"G\u2032":[179],"belongs":[180],"G.":[182],"say":[184],"k-probe-G":[190],"it":[192,207],"has":[193],"when":[199],"class":[203],"denominated":[209],"k-probe-split.":[210],"prove":[212],"deciding,":[214],"given":[215],"whether":[224],"h-probe-split":[228],"h":[232],"\u2264":[233],"NP-complete.":[236],"Besides,":[237],"by":[240],"subgraphs":[244],"2-probe-split":[246],"cographs":[247],"presented.":[249]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2023-09-16T00:00:00"}
