{"id":"https://openalex.org/W2076551320","doi":"https://doi.org/10.1145/2390176.2390187","title":"Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond","display_name":"Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2076551320","doi":"https://doi.org/10.1145/2390176.2390187","mag":"2076551320"},"language":"en","primary_location":{"id":"doi:10.1145/2390176.2390187","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2390176.2390187","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5031210702","display_name":"Geevarghese Philip","orcid":"https://orcid.org/0000-0003-0717-7303"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Geevarghese Philip","raw_affiliation_strings":["The Institute of Mathematical Sciences, Chennai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073311967","display_name":"Venkatesh Raman","orcid":"https://orcid.org/0000-0001-8123-0980"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Venkatesh Raman","raw_affiliation_strings":["The Institute of Mathematical Sciences, Chennai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079304468","display_name":"Somnath Sikdar","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Somnath Sikdar","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany","RWTH-Aachen University, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"RWTH-Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0599,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.91720808,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"9","issue":"1","first_page":"1","last_page":"23"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9973999857902527,"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":0.9962999820709229,"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/combinatorics","display_name":"Combinatorics","score":0.8403106927871704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7747533321380615},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5845761895179749},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.540265679359436},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5391132831573486},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4875430762767792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4842914938926697},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4599030017852783},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.45082685351371765},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.444386750459671},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.43236085772514343},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.428766131401062},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3593602180480957},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.13434135913848877}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8403106927871704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7747533321380615},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5845761895179749},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.540265679359436},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5391132831573486},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4875430762767792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4842914938926697},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4599030017852783},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.45082685351371765},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.444386750459671},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.43236085772514343},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.428766131401062},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3593602180480957},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.13434135913848877},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/2390176.2390187","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2390176.2390187","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.188.2725","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.2725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imsc.res.in/%7Evraman/pub/ds_kernel.pdf","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:217665","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/217665","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM transactions on algorithms : TALG 9(1), 11 (2012). doi:10.1145/2390176.2390187","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_1859613","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-C487-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W36639738","https://openalex.org/W121729551","https://openalex.org/W272982077","https://openalex.org/W1493071618","https://openalex.org/W1499709881","https://openalex.org/W1510730180","https://openalex.org/W1517036688","https://openalex.org/W1524652898","https://openalex.org/W1544829330","https://openalex.org/W1550062525","https://openalex.org/W1570425181","https://openalex.org/W1581552469","https://openalex.org/W1605439966","https://openalex.org/W1826380330","https://openalex.org/W1971799322","https://openalex.org/W1977374427","https://openalex.org/W2011039300","https://openalex.org/W2019284393","https://openalex.org/W2030711914","https://openalex.org/W2057205207","https://openalex.org/W2058258808","https://openalex.org/W2061881283","https://openalex.org/W2063493837","https://openalex.org/W2079313211","https://openalex.org/W2079444475","https://openalex.org/W2083748805","https://openalex.org/W2084389562","https://openalex.org/W2093762675","https://openalex.org/W2107284348","https://openalex.org/W2109410667","https://openalex.org/W2109542562","https://openalex.org/W2136829801","https://openalex.org/W2158584754","https://openalex.org/W2169262928","https://openalex.org/W2241818993","https://openalex.org/W2277497915","https://openalex.org/W2295651994","https://openalex.org/W2913688336","https://openalex.org/W2963253390","https://openalex.org/W4285719527","https://openalex.org/W4292230561","https://openalex.org/W6630973240"],"related_works":["https://openalex.org/W300018836","https://openalex.org/W3037291746","https://openalex.org/W2114815253","https://openalex.org/W3164644441","https://openalex.org/W3004945501","https://openalex.org/W2029114925","https://openalex.org/W641478897","https://openalex.org/W2898526288","https://openalex.org/W2002360843","https://openalex.org/W4286287454"],"abstract_inverted_index":{"We":[0,61],"show":[1,285],"that":[2,21,92,286],"for":[3,186,219,227,254,262,273,320],"every":[4],"fixed":[5,52],"j":[6,35,45,124,142],"\u2265":[7,9],"i":[8,33,43,127,131,145,149,317],"1,":[10],"the":[11,39,187,234,248,307,321],"k":[12,78,89,103,117,130,137,148,178,188,228,287,322],"-D":[13,189,229,288],"ominating":[14,190,230,289,326],"S":[15,191,231,290,327],"et":[16,192,232,291,328],"problem":[17,193,201,329],"restricted":[18],"to":[19],"graphs":[20,155,218,240,253,268],"do":[22,156],"not":[23,157,279],"have":[24,42,158],"K":[25,69,159,237,265,270,331],"ij":[26],"(the":[27,84],"complete":[28],"bipartite":[29],"graph":[30,72,82],"on":[31,170,194,330],"(":[32,179,315],"+":[34,125,128,143,146,174,181],")":[36,133,184,318],"vertices,":[37,46,134],"where":[38],"two":[40],"parts":[41],"and":[44,56,74,86,105,135,205,208,281,296],"respectively)":[47],"as":[48,161],"a":[49,58,63,68,75,81,96,110,162,167,221],"subgraph":[50],"is":[51,233],"parameter":[53],"tractable":[54],"(FPT)":[55],"has":[57,95,109,121,292],"polynomial":[59,168,222,297],"kernel.":[60],"describe":[62],"polynomial-time":[64],"algorithm":[65,258],"that,":[66],"given":[67],"i,j":[70,271,277,332],"-free":[71,272,333],"G":[73,94],"nonnegative":[76],"integer":[77,88],",":[79],"constructs":[80],"H":[83,108,120],"\u201ckernel\u201d)":[85],"an":[87,199,256,313],"'":[90,138],"such":[91],"(1)":[93],"dominating":[97,111],"set":[98,112],"of":[99,113,217,236,244,252,276,304],"size":[100,114],"at":[101,115],"most":[102,116,214,249],"if":[104,107],"only":[106],"',":[118],"(2)":[119],"O":[122,140,171,314],"((":[123,141,172],"1)":[126,144,182],"1":[129,147],"2":[132,150,183],"(3)":[136],"=":[139],").":[151],"Since":[152],"d":[153,173,176,180,195],"-degenerate":[154,196],"d+1,d+1":[160],"subgraph,":[163],"this":[164,263],"immediately":[165],"yields":[166],"kernel":[169,223],"2)":[175],"+2":[177],"vertices":[185],"graphs,":[197],"solving":[198],"open":[200],"posed":[202],"by":[203],"Alon":[204],"Gutner":[206,209,211],"[Alon":[207],"2008;":[210],"2009].":[212,242],"The":[213],"general":[215,250,302],"class":[216,235,251],"which":[220,255],"was":[224,259],"previously":[225,260],"known":[226,261],"h":[238,266],"-topological-minor-free":[239,267],"[Gutner":[241],"Graphs":[243],"bounded":[245],"degeneracy":[246],"are":[247,269],"FPT":[257,294],"problem.":[264],"suitable":[274],"values":[275],"(but":[278],"vice-versa),":[280],"so":[282],"our":[283],"results":[284],"both":[293],"algorithms":[295],"kernels":[298],"in":[299],"strictly":[300],"more":[301],"classes":[303],"graphs.":[305,334],"Using":[306],"same":[308],"techniques,":[309],"we":[310],"also":[311],"obtain":[312],"jk":[316],"vertex-kernel":[319],"-I":[323],"ndependent":[324],"D":[325]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":32},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}