{"id":"https://openalex.org/W2167914060","doi":"https://doi.org/10.1002/malq.19970430102","title":"Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second \u2010 Order Logic","display_name":"Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second \u2010 Order Logic","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2167914060","doi":"https://doi.org/10.1002/malq.19970430102","mag":"2167914060"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430102","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430102","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5061350983","display_name":"Iain A. Stewart","orcid":"https://orcid.org/0000-0002-0752-1971"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Iain A. Stewart","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061350983"],"corresponding_institution_ids":["https://openalex.org/I153648349"],"apc_list":{"value":2900,"currency":"USD","value_usd":2900},"apc_paid":null,"fwci":0.5107,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68863728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9955999851226807,"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/T11567","display_name":"semigroups and automata theory","score":0.9955999851226807,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9944999814033508,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8134959936141968},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8107432126998901},{"id":"https://openalex.org/keywords/monadic-predicate-calculus","display_name":"Monadic predicate calculus","score":0.6672306656837463},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.538223385810852},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5187842845916748},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5036186575889587},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5009288787841797},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.43359264731407166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09516778588294983},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.06426575779914856}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8134959936141968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8107432126998901},{"id":"https://openalex.org/C124656256","wikidata":"https://www.wikidata.org/wiki/Q6897882","display_name":"Monadic predicate calculus","level":4,"score":0.6672306656837463},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.538223385810852},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5187842845916748},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5036186575889587},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5009288787841797},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.43359264731407166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09516778588294983},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.06426575779914856},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430102","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430102","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W126455252","https://openalex.org/W189149083","https://openalex.org/W200063938","https://openalex.org/W657835803","https://openalex.org/W1501455971","https://openalex.org/W1555138513","https://openalex.org/W1566033350","https://openalex.org/W1651830791","https://openalex.org/W1812706522","https://openalex.org/W1942096134","https://openalex.org/W1970629906","https://openalex.org/W1976534954","https://openalex.org/W1979904465","https://openalex.org/W2003895694","https://openalex.org/W2011039300","https://openalex.org/W2023552332","https://openalex.org/W2031411912","https://openalex.org/W2033743662","https://openalex.org/W2039302045","https://openalex.org/W2043438634","https://openalex.org/W2043507528","https://openalex.org/W2075322882","https://openalex.org/W2125362004","https://openalex.org/W2138709937","https://openalex.org/W2140509943","https://openalex.org/W3105529609","https://openalex.org/W4388299483"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1668658774","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W2168900540","https://openalex.org/W4286911546","https://openalex.org/W4290190164"],"abstract_inverted_index":{"Abstract":[0],"We":[1,122],"investigate":[2],"the":[3,10,42,75,96,108,158],"definability":[4,159],"in":[5,51,150],"monadic":[6,8,124,129,151,153,164,166],"\u221111and":[7,152,165],"\u03a011of":[9],"problems":[11,147,162],"REGk,":[12],"of":[13,20,27,39,98,110,160],"whether":[14,99,111,145],"there":[15,34],"is":[16,35,95,103,107],"a":[17,30,36,100,112,116,132],"regular":[18,37],"subgraph":[19,38],"degreekin":[21,40],"some":[22],"given":[23,31,101,113,120],"graph,":[24,33],"and":[25,46,88,105,131,139,155],"XREGk,":[26],"whether,":[28],"for":[29],"rooted":[32],"which":[41,52],"root":[43],"has":[44,55,115],"degreek,":[45],"their":[47,168],"restrictions":[48],"to":[49,86,136,141,177],"graphs":[50,67],"every":[53],"vertex":[54],"degree":[56],"at":[57],"mostk,":[58],"namely":[59],"REGkkand":[60,82],"XREGkk,":[61],"respectively,":[62,90],"fork\u2265":[63,91],"2":[64],"(all":[65],"our":[66],"are":[68,148],"undirected).":[69],"Our":[70],"motivation":[71],"partly":[72],"stems":[73],"from":[74,173],"fact":[76],"(which":[77,171],"we":[78,156],"prove":[79],"here)":[80],"that":[81],"XREGkkare":[83],"logspace":[84,176],"equivalent":[85],"CONN":[87,94],"REACH,":[89],"3,":[92],"where":[93],"problem":[97,109],"graph":[102,114],"connected":[104],"REACH":[106],"path":[117],"joining":[118],"two":[119],"vertices.":[121],"use":[123],"first":[125],"\u2010":[126,179],"order":[127],"reductions,":[128],"\u221111games":[130],"recent":[133],"technique":[134],"due":[135],"Fagin,":[137],"Stockmeyer":[138],"Vardi":[140],"almost":[142],"completely":[143],"classify":[144],"these":[146,161],"definable":[149],"\u03a011,":[154],"compare":[157],"(in":[163],"\u03a011with":[167],"computational":[169],"complexity":[170],"varies":[172],"solvable":[174],"using":[175],"NP":[178],"complete).":[180]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
