{"id":"https://openalex.org/W4385782261","doi":"https://doi.org/10.1007/s00224-023-10135-x","title":"The Parameterized Complexity of\u00a0s-Club with Triangle and Seed Constraints","display_name":"The Parameterized Complexity of\u00a0s-Club with Triangle and Seed Constraints","publication_year":2023,"publication_date":"2023-08-12","ids":{"openalex":"https://openalex.org/W4385782261","doi":"https://doi.org/10.1007/s00224-023-10135-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-023-10135-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10135-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10135-x.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10135-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083385671","display_name":"Jaroslav Garvardt","orcid":"https://orcid.org/0000-0002-8762-8567"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jaroslav Garvardt","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8762-8567","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087168202","display_name":"Christian Komusiewicz","orcid":"https://orcid.org/0000-0003-0829-7032"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Komusiewicz","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0829-7032","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027185367","display_name":"Frank Sommer","orcid":"https://orcid.org/0000-0003-4034-525X"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank Sommer","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4034-525X","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083385671"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.1427,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.47645794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"67","issue":"5","first_page":"1050","last_page":"1081"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9947999715805054,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9944000244140625,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.7091395258903503},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6587912440299988},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5514124035835266},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5172222852706909},{"id":"https://openalex.org/keywords/club","display_name":"Club","score":0.5166164040565491},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5055997371673584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43458080291748047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36454468965530396},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07054033875465393}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7091395258903503},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6587912440299988},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5514124035835266},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5172222852706909},{"id":"https://openalex.org/C2776459890","wikidata":"https://www.wikidata.org/wiki/Q3297812","display_name":"Club","level":2,"score":0.5166164040565491},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5055997371673584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43458080291748047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36454468965530396},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07054033875465393},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00224-023-10135-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10135-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10135-x.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00224-023-10135-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10135-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10135-x.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3072270648","display_name":null,"funder_award_id":"KO 3669/6","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3184373142","display_name":null,"funder_award_id":"KO 3669/6-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3966283350","display_name":null,"funder_award_id":"EAGR (KO 3669/6-1)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385782261.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1980096229","https://openalex.org/W1988659376","https://openalex.org/W2010661649","https://openalex.org/W2016182558","https://openalex.org/W2051438793","https://openalex.org/W2061931042","https://openalex.org/W2066090568","https://openalex.org/W2089494972","https://openalex.org/W2092080501","https://openalex.org/W2100978151","https://openalex.org/W2107284348","https://openalex.org/W2110160472","https://openalex.org/W2116087731","https://openalex.org/W2292553316","https://openalex.org/W2300144455","https://openalex.org/W2425914729","https://openalex.org/W2615011235","https://openalex.org/W2883786747","https://openalex.org/W2914414140","https://openalex.org/W2953865418","https://openalex.org/W2962860656","https://openalex.org/W4308243711"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W1976468483","https://openalex.org/W2480116122","https://openalex.org/W3179905963","https://openalex.org/W1516574938","https://openalex.org/W2563912921"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"s":[2,41,47,139],"-":[3,48,140],"Club":[4,49,141],"problem":[5],"asks":[6],"whether":[7],"a":[8,14,108,185],"given":[9,109],"undirected":[10],"graph":[11,176],"G":[12,25,32,58,75,83,100,171],"contains":[13,107],"vertex":[15,56],"set":[16,110,180],"S":[17,27,35,60,77,85,102,106],"of":[18,31,46,57,82,112,181],"size":[19,129],"at":[20,39,65,90],"least":[21,66,91],"k":[22,130],"such":[23],"that":[24,54,79,105,117],"[":[26,59,76,84,101,172],"],":[28,78,103,174],"the":[29,127,137,144,153,168,175,179],"subgraph":[30],"induced":[33,177],"by":[34,126,178],",":[36,131],"has":[37],"diameter":[38],"most":[40],".":[42],"We":[43,115],"consider":[44],"variants":[45,121],"where":[50],"one":[51],"additionally":[52],"demands":[53],"each":[55,80],"]":[61,86],"is":[62,87,184],"contained":[63,88],"in":[64,74,89,99,118],"$$\\ell":[67,92,156],"$$":[68,93],"<mml:math":[69,94,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[70,95,159],"<mml:mi>\u2113</mml:mi>":[71,96,161],"</mml:math>":[72,97,165],"triangles":[73,98],"edge":[81],"or":[104],"W":[111,173],"seed":[113,182],"vertices.":[114],"show":[116],"general":[119],"these":[120],"are":[122],"W[1]-hard":[123],"when":[124,155,170],"parameterized":[125],"solution":[128],"making":[132],"them":[133],"significantly":[134],"harder":[135],"than":[136],"unconstrained":[138],"problem.":[142],"On":[143],"positive":[145],"side,":[146],"we":[147],"obtain":[148],"some":[149],"FPT":[150],"algorithms":[151],"for":[152,167],"case":[154,169],"=1$$":[157],"<mml:mrow>":[160],"<mml:mo>=</mml:mo>":[162],"<mml:mn>1</mml:mn>":[163],"</mml:mrow>":[164],"and":[166],"vertices,":[183],"clique.":[186]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
