{"id":"https://openalex.org/W3133677238","doi":"https://doi.org/10.1007/s00453-022-01088-7","title":"Essentially Tight Kernels for (Weakly) Closed Graphs","display_name":"Essentially Tight Kernels for (Weakly) Closed Graphs","publication_year":2023,"publication_date":"2023-01-09","ids":{"openalex":"https://openalex.org/W3133677238","doi":"https://doi.org/10.1007/s00453-022-01088-7","mag":"3133677238"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-022-01088-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-022-01088-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-01088-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","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/s00453-022-01088-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088434500","display_name":"Tomohiro Koana","orcid":"https://orcid.org/0000-0002-8684-0611"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tomohiro Koana","raw_affiliation_strings":["Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, 10623, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8684-0611","affiliations":[{"raw_affiliation_string":"Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"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":true,"raw_author_name":"Christian Komusiewicz","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, 35037, Marburg, Hessia, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0829-7032","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, 35037, Marburg, Hessia, 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, 35037, Marburg, Hessia, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4034-525X","affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, 35037, Marburg, Hessia, Germany","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087168202"],"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":0.1436,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.41702875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"85","issue":"6","first_page":"1706","last_page":"1735"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9991000294685364,"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/T10083","display_name":"Graphene research and applications","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6124764680862427},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35232627391815186},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33911043405532837}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6124764680862427},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35232627391815186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33911043405532837}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-022-01088-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-022-01088-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-01088-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00453-022-01088-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00453-022-01088-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-01088-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G100663255","display_name":null,"funder_award_id":"NI 369/21","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"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"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3133677238.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W57303768","https://openalex.org/W184144034","https://openalex.org/W200056458","https://openalex.org/W285041758","https://openalex.org/W1485742133","https://openalex.org/W1488421129","https://openalex.org/W1821538950","https://openalex.org/W2007044730","https://openalex.org/W2016341899","https://openalex.org/W2030711914","https://openalex.org/W2052712469","https://openalex.org/W2057205207","https://openalex.org/W2059738021","https://openalex.org/W2064197162","https://openalex.org/W2076551320","https://openalex.org/W2090698092","https://openalex.org/W2107284348","https://openalex.org/W2116087731","https://openalex.org/W2133839241","https://openalex.org/W2144047548","https://openalex.org/W2151566751","https://openalex.org/W2153676433","https://openalex.org/W2241275978","https://openalex.org/W2277497915","https://openalex.org/W2914414140","https://openalex.org/W3019028961","https://openalex.org/W3042137000","https://openalex.org/W3042736922","https://openalex.org/W3082339973","https://openalex.org/W3098486139","https://openalex.org/W4309757100"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"kernelization":[3,165,206,342],"of":[4,66,74,101,166,185,230,284,304,343],"classic":[5],"hard":[6],"graph":[7,68,293],"problems":[8,168,179],"when":[9,321],"the":[10,21,49,72,98,164,341],"input":[11],"graphs":[12,210,347,362],"fulfill":[13],"triadic":[14],"closure":[15,25,30,58,76,350],"properties.":[16],"More":[17],"precisely,":[18],"we":[19,96,224,254,276,336],"consider":[20],"recently":[22],"introduced":[23],"parameters":[24],"number":[26,31,59,77,351],"c":[27,78,352],"and":[28,79,93,135,331,353,363],"weak":[29,57],"$$\\gamma":[32,60],"$$":[33,61],"<mml:math":[34,62,106,122,140,189,233,261,297,309,324],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[35,63,107,123,141,190,234,262,298,310,325],"<mml:mi>\u03b3</mml:mi>":[36,64,113,129,145,152,196,316],"</mml:math>":[37,65,117,133,156,200,244,273,300,320,327],"(Fox":[38],"et":[39,212],"al.":[40,213],"SIAM":[41],"J":[42],"Comput":[43],"49(2):448\u2013464,":[44],"2020)":[45],"in":[46],"addition":[47],"to":[48,182,290],"standard":[50],"parameter":[51],"solution":[52],"size":[53,102,186,231,305],"k":[54,288],".":[55,83],"The":[56],"a":[67,228,256,291,302],"is":[69,245],"upper-bounded":[70],"by":[71,201],"minimum":[73],"its":[75,80],"degeneracy":[81],"d":[82],"For":[84,219],"Capacitated":[85,220],"Vertex":[86,90,221,251],"Cover":[87,91,222,252],",":[88,92,118,134,157,223,253],"Connected":[89,250],"Induced":[94],"Matching":[95],"obtain":[97,255],"first":[99],"kernels":[100,173,184,354],"$$k^{\\mathcal":[103,119,306],"{O}(\\gamma":[104,120,138,307],")}$$":[105,121,139,188,308],"<mml:msup>":[108,124,142,191,235,267,311],"<mml:mi>k</mml:mi>":[109,125,146,192,236,268,312],"<mml:mrow>":[110,126,143,149,193,237,263,313],"<mml:mi>O</mml:mi>":[111,127,150,264,314],"<mml:mo>(</mml:mo>":[112,128,144,151,195,239,265,315],"<mml:mo>)</mml:mo>":[114,130,147,153,197,241,271,317],"</mml:mrow>":[115,131,148,154,198,242,272,318],"</mml:msup>":[116,132,155,199,243,270,319],"$$(\\gamma":[136],"k)^{\\mathcal":[137],"respectively.":[158],"This":[159],"extends":[160],"previous":[161,202],"results":[162,203],"on":[163,169,204,208,346,358],"these":[167,178],"degenerate":[170,209],"graphs.":[171,334,367],"These":[172],"are":[174,180],"essentially":[175],"tight":[176],"as":[177],"unlikely":[181],"admit":[183],"$$k^{o(\\gamma":[187],"<mml:mi>o</mml:mi>":[194,238],"their":[205],"complexity":[207],"(Cygan":[211],"ACM":[214],"Trans":[215],"Algorithms":[216],"13(3):43:1\u201343:22,":[217],"2017).":[218],"show":[225],"that":[226,278],"even":[227],"kernel":[229,257,303],"$$k^{o(c)}$$":[232],"<mml:mi>c</mml:mi>":[240,266],"unlikely.":[246],"In":[247],"contrast,":[248],"for":[249,280,340,355],"with":[258,348],"$$\\mathcal":[259,295,322],"{O}(ck^2)$$":[260],"<mml:mn>2</mml:mn>":[269],"vertices.":[274],"Moreover,":[275],"prove":[277],"searching":[279],"an":[281],"induced":[282],"subgraph":[283],"order":[285],"at":[286],"least":[287],"belonging":[289],"hereditary":[292],"class":[294],"{G}$$":[296,323],"<mml:mi>G</mml:mi>":[299,326],"admits":[301],"contains":[328],"all":[329,332],"complete":[330],"edgeless":[333],"Finally,":[335],"provide":[337],"lower":[338],"bounds":[339],"Independent":[344],"Set":[345,357],"constant":[349],"Dominating":[356],"weakly":[359,364],"closed":[360,365],"split":[361],"bipartite":[366]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}