{"id":"https://openalex.org/W1983652976","doi":"https://doi.org/10.1137/09077850x","title":"Maximum $r$-Regular Induced Subgraph Problem: Fast Exponential Algorithms and Combinatorial Bounds","display_name":"Maximum $r$-Regular Induced Subgraph Problem: Fast Exponential Algorithms and Combinatorial Bounds","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1983652976","doi":"https://doi.org/10.1137/09077850x","mag":"1983652976"},"language":"en","primary_location":{"id":"doi:10.1137/09077850x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077850x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5076062797","display_name":"Sushmita Gupta","orcid":"https://orcid.org/0000-0003-1255-8266"},"institutions":[{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sushmita Gupta","raw_affiliation_strings":["Computer Science, Department of Mathematics and Computer Science (IMADA)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Department of Mathematics and Computer Science (IMADA)","institution_ids":["https://openalex.org/I4210156583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073311967","display_name":"Venkatesh Raman","orcid":"https://orcid.org/0000-0001-8123-0980"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Venkatesh Raman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7798,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.96403593,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"4","first_page":"1758","last_page":"1780"},"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":0.9997000098228455,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.7517784833908081},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6331697106361389},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6141820549964905},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4872962236404419},{"id":"https://openalex.org/keywords/combinatorial-algorithms","display_name":"Combinatorial algorithms","score":0.4449719786643982},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4370948076248169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7517784833908081},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6331697106361389},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6141820549964905},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4872962236404419},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.4449719786643982},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4370948076248169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/09077850x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077850x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:sdu.dk:openaire_cris_publications/169c389e-4ac0-4660-97b8-7d14d278c8f1","is_oa":false,"landing_page_url":"https://portal.findresearcher.sdu.dk/da/publications/169c389e-4ac0-4660-97b8-7d14d278c8f1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400423","display_name":"University of Southern Denmark Research Portal (University of Southern Denmark)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177969490","host_organization_name":"University of Southern Denmark","host_organization_lineage":["https://openalex.org/I177969490"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Gupta, S, Raman, V & Saurabh, S 2012, 'MAXIMUM r-REGULAR INDUCED SUBGRAPH PROBLEM: FAST EXPONENTIAL ALGORITHMS AND COMBINATORIAL BOUNDS', SIAM Journal on Discrete Mathematics, vol. 26, no. 4, pp. 1758-1780. https://doi.org/10.1137/09077850x","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1974672137","https://openalex.org/W2004006145","https://openalex.org/W2007200873","https://openalex.org/W2013568176","https://openalex.org/W2035700242","https://openalex.org/W2044104853","https://openalex.org/W2047470084","https://openalex.org/W2047747666","https://openalex.org/W2065003601","https://openalex.org/W2068155033","https://openalex.org/W2073025989","https://openalex.org/W2085870956","https://openalex.org/W2089718638","https://openalex.org/W2119626000","https://openalex.org/W2122639972","https://openalex.org/W2138017804","https://openalex.org/W2149624304","https://openalex.org/W2159177140","https://openalex.org/W4210377846","https://openalex.org/W4244894548"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4409439182","https://openalex.org/W2053286651","https://openalex.org/W2980963558","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378"],"abstract_inverted_index":{"We":[0,65],"show":[1],"that":[2,119,152],"for":[3,142,173,176,207],"a":[4,28,60,89,122,128,143,161,169,184,208,227],"fixed":[5,178],"$r$,":[6,180],"the":[7,38,53,79,106,134,153,164,194,200,212,218,229,235],"number":[8,54,80],"of":[9,41,50,55,59,81,120,146,163,211],"maximal":[10,56,83,107],"$r$-regular":[11,84,108,124],"induced":[12,85,109,125,154],"subgraphs":[13,86,110],"in":[14,88,111,199],"any":[15,177],"graph":[16,61,90,129],"with":[17],"$n$":[18,63,92,132],"vertices":[19],"is":[20,27,118,158,183,226],"upper":[21,48,68,95],"bounded":[22],"by":[23,71],"$\\mathcal{O}(c^n)$,":[24],"where":[25,181,224],"$c$":[26,182],"positive":[29,185],"constant":[30,179,186],"strictly":[31,187],"less":[32,188],"than":[33,189],"$2$.":[34,190],"This":[35],"bound":[36,49,69,77,96],"generalizes":[37],"well-known":[39],"result":[40,70],"Moon":[42],"and":[43,196,234],"Moser,":[44],"who":[45],"showed":[46],"an":[47,73],"$3^{n/3}$":[51],"on":[52,62,78,91,131,156],"independent":[57],"sets":[58],"vertices.":[64,93],"complement":[66],"this":[67,174],"obtaining":[72],"almost":[74],"tight":[75],"lower":[76],"(possible)":[82],"possible":[87],"Our":[94],"results":[97,197],"are":[98],"algorithmic.":[99],"That":[100],"is,":[101],"we":[102,167,192],"can":[103],"enumerate":[104],"all":[105],"time":[112,171],"$\\mathcal{O}(c^n":[113],"n^{\\mathcal{O}(1)})$.":[114],"A":[115],"related":[116],"question":[117],"finding":[121],"maximum-sized":[123,144],"subgraph.":[126],"Given":[127],"$G=(V,E)$":[130],"vertices,":[133,147],"Maximum":[135,231],"$r$-Regular":[136,220],"Induced":[137,213,219],"Subgraph":[138,214,221],"(M-$r$-RIS)":[139],"problem":[140,175,233],"asks":[141],"subset":[145],"$R":[148],"\\subseteq":[149],"V$,":[150],"such":[151],"subgraph":[155],"$R$":[157],"$r$-regular.":[159],"As":[160],"by-product":[162],"enumeration":[165],"algorithm,":[166],"get":[168],"$\\mathcal{O}(c^n)$":[170],"algorithm":[172],"Furthermore,":[191],"use":[193],"techniques":[195],"obtained":[198],"paper":[201],"to":[202],"obtain":[203],"improved":[204],"exact":[205],"algorithms":[206],"special":[209],"case":[210],"Isomorphism":[215,222],"problem,":[216,223],"namely,":[217],"$r$":[225],"constant,":[228],"$\\delta$-Separating":[230],"Matching":[232],"Efficient":[236],"Edge":[237],"Dominating":[238],"Set":[239],"problem.":[240]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
