{"id":"https://openalex.org/W2037713618","doi":"https://doi.org/10.1137/120892234","title":"Structure Theorem and Isomorphism Test for Graphs with Excluded Topological Subgraphs","display_name":"Structure Theorem and Isomorphism Test for Graphs with Excluded Topological Subgraphs","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2037713618","doi":"https://doi.org/10.1137/120892234","mag":"2037713618"},"language":"en","primary_location":{"id":"doi:10.1137/120892234","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120892234","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5073893026","display_name":"Martin Grohe","orcid":"https://orcid.org/0000-0002-0292-9142"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]},{"id":"https://openalex.org/I4210117195","display_name":"Institute for Computer Science and Control","ror":"https://ror.org/0249v7n71","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]}],"countries":["DE","HU"],"is_corresponding":true,"raw_author_name":"Martin Grohe","raw_affiliation_strings":["Institut f\u00fcr Informatik Humboldt-Universit\u00e4t zu Berlin Berlin, Germany","Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik Humboldt-Universit\u00e4t zu Berlin Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary","institution_ids":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012849997","display_name":"D\u00e1niel Marx","orcid":"https://orcid.org/0000-0002-5686-8314"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]},{"id":"https://openalex.org/I4210117195","display_name":"Institute for Computer Science and Control","ror":"https://ror.org/0249v7n71","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]}],"countries":["DE","HU"],"is_corresponding":false,"raw_author_name":"D\u00e1niel Marx","raw_affiliation_strings":["Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary","Institut f\u00fcr Informatik Humboldt-Universit\u00e4t zu Berlin Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary","institution_ids":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik Humboldt-Universit\u00e4t zu Berlin Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073893026"],"corresponding_institution_ids":["https://openalex.org/I39343248","https://openalex.org/I4210117195","https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":11.2166,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.9881376,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"44","issue":"1","first_page":"114","last_page":"159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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":0.9980000257492065,"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":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7681538462638855},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6823680996894836},{"id":"https://openalex.org/keywords/subgraph-isomorphism-problem","display_name":"Subgraph isomorphism problem","score":0.6727859377861023},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.6456227898597717},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5421143770217896},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.44955170154571533},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.44449955224990845},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.42777159810066223},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.42361193895339966},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.29220956563949585},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20115947723388672},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.09735473990440369}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7681538462638855},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6823680996894836},{"id":"https://openalex.org/C131992880","wikidata":"https://www.wikidata.org/wiki/Q2528185","display_name":"Subgraph isomorphism problem","level":3,"score":0.6727859377861023},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.6456227898597717},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5421143770217896},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.44955170154571533},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.44449955224990845},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.42777159810066223},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.42361193895339966},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.29220956563949585},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20115947723388672},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.09735473990440369},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120892234","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120892234","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W10105891","https://openalex.org/W132145278","https://openalex.org/W179577048","https://openalex.org/W1553391053","https://openalex.org/W1967546560","https://openalex.org/W1973322735","https://openalex.org/W1974672137","https://openalex.org/W1987393587","https://openalex.org/W1991543902","https://openalex.org/W1998811202","https://openalex.org/W2005079828","https://openalex.org/W2013522700","https://openalex.org/W2016588822","https://openalex.org/W2021156120","https://openalex.org/W2026005637","https://openalex.org/W2039732465","https://openalex.org/W2045027298","https://openalex.org/W2047871605","https://openalex.org/W2067016370","https://openalex.org/W2075516513","https://openalex.org/W2078674325","https://openalex.org/W2112686605","https://openalex.org/W2115607023","https://openalex.org/W2119044694","https://openalex.org/W2121641644","https://openalex.org/W2129907634","https://openalex.org/W2130481157","https://openalex.org/W2159366821","https://openalex.org/W2160167461","https://openalex.org/W2253740506","https://openalex.org/W2950291041","https://openalex.org/W2991385428"],"related_works":["https://openalex.org/W2962884946","https://openalex.org/W2032950096","https://openalex.org/W2089369802","https://openalex.org/W2550699029","https://openalex.org/W4299790368","https://openalex.org/W2949444937","https://openalex.org/W1744680276","https://openalex.org/W3198137016","https://openalex.org/W2953172827","https://openalex.org/W2571406257"],"abstract_inverted_index":{"We":[0,27,89],"generalize":[1],"the":[2,62,100,107,224],"structure":[3,96,108,221],"theorem":[4,222],"of":[5,64,68,94,102,106,174,213,219,226],"Robertson":[6],"and":[7,164,190],"Seymour":[8],"for":[9,30],"graphs":[10,20,114,146,178,193],"excluding":[11,21,36,115,147],"a":[12,17,24,31,39,43,54,65,75,103,118,150,217],"fixed":[13,32,55],"graph":[14,35],"$H$":[15,22,37,116,148],"as":[16,23,38,117,149],"minor":[18],"to":[19,53,223],"topological":[25,40,119,151],"subgraph.":[26],"prove":[28,72],"that":[29,73,82,112,144],"$H$,":[33],"every":[34],"subgraph":[41],"has":[42,58,130],"tree":[44],"decomposition":[45,76],"where":[46],"each":[47],"part":[48],"is":[49,77,83],"either":[50],"\"almost":[51],"embeddable\"":[52],"surface":[56],"or":[57],"bounded":[59,66],"degree":[60],"with":[61,86],"exception":[63],"number":[67],"vertices.":[69],"Furthermore,":[70],"we":[71,110,142],"such":[74],"computable":[78],"by":[79],"an":[80],"algorithm":[81],"fixed-parameter":[84],"tractable":[85],"parameter":[87],"$|H|$.":[88],"present":[90],"two":[91,166],"algorithmic":[92],"applications":[93],"our":[95,220],"theorem.":[97],"To":[98],"illustrate":[99],"mechanics":[101],"\"typical\"":[104],"application":[105],"theorem,":[109],"show":[111,143],"on":[113,145],"subgraph,":[120,152],"Partial":[121],"Dominating":[122],"Set":[123],"(find":[124],"$k$":[125],"vertices":[126],"whose":[127],"closed":[128],"neighborhood":[129],"maximum":[131],"size)":[132],"can":[133,155],"be":[134,156],"solved":[135,157],"in":[136,158],"time":[137,159,171],"$f(H,k)\\cdot":[138],"n^{O(1)}$.":[139],"More":[140],"significantly,":[141],"Graph":[153,175],"Isomorphism":[154],"$n^{f(H)}$.":[160],"This":[161],"result":[162,215],"unifies":[163],"generalizes":[165],"previously":[167],"known":[168],"important":[169],"polynomial":[170],"solvable":[172],"cases":[173],"Isomorphism:":[176],"bounded-degree":[177],"[E.":[179],"M.":[180],"Luks,":[181],"J.":[182],"Comput.":[183],"System":[184],"Sci.,":[185],"25":[186],"(1982),":[187],"pp.":[188,208],"42--65]":[189],"$H$-minor":[191],"free":[192],"[I.":[194],"N.":[195],"Ponomarenko,":[196],"Zap.":[197],"Nauchn.":[198],"Sem.":[199],"Leningrad.":[200],"Otdel.":[201],"Mat.":[202],"Inst.":[203],"Steklov.":[204],"(LOMI),":[205],"174":[206],"(1988),":[207],"147--177,":[209],"182].":[210],"The":[211],"proof":[212],"this":[214],"needs":[216],"generalization":[218],"context":[225],"invariant":[227],"treelike":[228],"decomposition.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}