{"id":"https://openalex.org/W2952529636","doi":"https://doi.org/10.1137/19m1245293","title":"A Faster Isomorphism Test for Graphs of Small Degree","display_name":"A Faster Isomorphism Test for Graphs of Small Degree","publication_year":2020,"publication_date":"2020-02-19","ids":{"openalex":"https://openalex.org/W2952529636","doi":"https://doi.org/10.1137/19m1245293","mag":"2952529636"},"language":"en","primary_location":{"id":"doi:10.1137/19m1245293","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245293","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.04659","any_repository_has_fulltext":true},"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/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":true,"raw_author_name":"Martin Grohe","raw_affiliation_strings":["RWTH Aachen University"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008306814","display_name":"Daniel Neuen","orcid":"https://orcid.org/0000-0002-4940-0318"},"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":"Daniel Neuen","raw_affiliation_strings":["RWTH Aachen University"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017685495","display_name":"Pascal Schweitzer","orcid":"https://orcid.org/0009-0001-3585-8213"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pascal Schweitzer","raw_affiliation_strings":["University of Kaiserslautern"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073893026"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.1443,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48504895,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"6","first_page":"FOCS18","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9993000030517578,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/graph-isomorphism","display_name":"Graph isomorphism","score":0.8462847471237183},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.818252682685852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7832080125808716},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7806799411773682},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7112029790878296},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5149310231208801},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44926756620407104},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10007929801940918}],"concepts":[{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.8462847471237183},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.818252682685852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7832080125808716},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7806799411773682},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7112029790878296},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5149310231208801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44926756620407104},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10007929801940918},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1245293","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245293","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"},{"id":"pmh:oai:arXiv.org:1802.04659","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.04659","pdf_url":"https://arxiv.org/pdf/1802.04659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2952529636","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.04659.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:publications.rwth-aachen.de:752231","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/752231","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","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":"IEEE 89-100 (2018). doi:10.1109/FOCS.2018.00018","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1802.04659","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.04659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.04659","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.04659","pdf_url":"https://arxiv.org/pdf/1802.04659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2952529636.pdf","grobid_xml":"https://content.openalex.org/works/W2952529636.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W12766527","https://openalex.org/W618980177","https://openalex.org/W656473322","https://openalex.org/W968917338","https://openalex.org/W1493654001","https://openalex.org/W1967307108","https://openalex.org/W1973322735","https://openalex.org/W1974672137","https://openalex.org/W1987393587","https://openalex.org/W1991005941","https://openalex.org/W1996938202","https://openalex.org/W2017265236","https://openalex.org/W2037713618","https://openalex.org/W2044263342","https://openalex.org/W2044443711","https://openalex.org/W2081256177","https://openalex.org/W2090590511","https://openalex.org/W2091293447","https://openalex.org/W2092884496","https://openalex.org/W2096418375","https://openalex.org/W2102756649","https://openalex.org/W2120980679","https://openalex.org/W2162763810","https://openalex.org/W2164314258","https://openalex.org/W2190928263","https://openalex.org/W2396266074","https://openalex.org/W2409645877","https://openalex.org/W2593190625","https://openalex.org/W2963366865","https://openalex.org/W4230191592","https://openalex.org/W4233378042","https://openalex.org/W4234295943"],"related_works":["https://openalex.org/W2213292345","https://openalex.org/W3108904375","https://openalex.org/W3185162868","https://openalex.org/W3110267038","https://openalex.org/W3162333725","https://openalex.org/W2145937415","https://openalex.org/W151079317","https://openalex.org/W3170119558","https://openalex.org/W1778521510","https://openalex.org/W2012000897","https://openalex.org/W2759913242","https://openalex.org/W562742013","https://openalex.org/W2110787567","https://openalex.org/W2899364936","https://openalex.org/W1995077491","https://openalex.org/W2054018639","https://openalex.org/W3163318818","https://openalex.org/W2963468679","https://openalex.org/W2625453034","https://openalex.org/W2963204649"],"abstract_inverted_index":{"In":[0,20],"a":[1,15],"recent":[2],"breakthrough,":[3],"Babai":[4],"[Proceedings":[5,84],"of":[6,31,46,48,57,74,85],"STOC,":[7],"ACM,":[8],"New":[9,88],"York,":[10,89],"2016,":[11],"pp.":[12,91],"684--697]":[13],"gave":[14],"quasipolynomial-time":[16],"graph":[17],"isomorphism":[18,27,70],"test.":[19],"this":[21],"work,":[22],"we":[23],"give":[24],"an":[25,64],"improved":[26],"test":[28,71],"for":[29,72],"graphs":[30,73],"small":[32],"degree:":[33],"our":[34],"algorithm":[35],"runs":[36,93],"in":[37,94],"time":[38,95],"$n^{\\mathcal{O}((\\log":[39],"d)^{c})}$,":[40],"where":[41],"$n$":[42],"is":[43,53,63],"the":[44,49,54,58],"number":[45],"vertices":[47],"input":[50,59],"graphs,":[51,60],"$d$":[52,77],"maximum":[55,75],"degree":[56,76],"and":[61,82],"$c$":[62],"absolute":[65],"constant.":[66],"The":[67],"best":[68],"previous":[69],"due":[78],"to":[79],"Babai,":[80],"Kantor,":[81],"Luks":[83],"FOCS,":[86],"IEEE,":[87],"1983,":[90],"162--171]":[92],"$n^{\\mathcal{O}(d/":[96],"\\log":[97],"d)}$.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}