{"id":"https://openalex.org/W2803836358","doi":"https://doi.org/10.4230/lipics.icalp.2018.40","title":"Lov\u00e1sz Meets Weisfeiler and Leman","display_name":"Lov\u00e1sz Meets Weisfeiler and Leman","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2803836358","doi":"https://doi.org/10.4230/lipics.icalp.2018.40","mag":"2803836358"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1802.08876","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.08876","pdf_url":"https://arxiv.org/pdf/1802.08876","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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.08876","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052689442","display_name":"Holger Dell","orcid":"https://orcid.org/0000-0001-8955-0786"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dell, Holger","raw_affiliation_strings":["Saarland University and Cluster of Excellence (MMCI), Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University and Cluster of Excellence (MMCI), Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","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":false,"raw_author_name":"Grohe, Martin","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087543886","display_name":"Gaurav Rattan","orcid":"https://orcid.org/0000-0002-5095-860X"},"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":"Rattan, Gaurav","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052689442"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":1.29944285,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8033242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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":0.9933000206947327,"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/homomorphism","display_name":"Homomorphism","score":0.6967799663543701},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6630932688713074},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5082008838653564},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4894186556339264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4710036814212799},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.45443007349967957}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6967799663543701},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6630932688713074},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5082008838653564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4894186556339264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4710036814212799},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.45443007349967957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1802.08876","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.08876","pdf_url":"https://arxiv.org/pdf/1802.08876","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1802.08876","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.08876","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.icalp.2018.40","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2018.40","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.08876","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.08876","pdf_url":"https://arxiv.org/pdf/1802.08876","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W64175367","https://openalex.org/W1539677952","https://openalex.org/W2109294083","https://openalex.org/W2111302825","https://openalex.org/W2142498761","https://openalex.org/W2147377644","https://openalex.org/W2409645877","https://openalex.org/W2911738047"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4308159138","https://openalex.org/W4327811209","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W3037616202","https://openalex.org/W2963079901","https://openalex.org/W2990092783","https://openalex.org/W1878187357","https://openalex.org/W47340958"],"abstract_inverted_index":{"In":[0],"this":[1,97],"paper,":[2],"we":[3,127,135,216],"relate":[4],"a":[5,11,75,142,201,227,243],"beautiful":[6],"theory":[7],"by":[8,44],"Lov\u00e1sz":[9],"with":[10,246],"popular":[12],"heuristic":[13],"algorithm":[14,24,48,116,230],"for":[15,53,71,137,153,170,204,234],"the":[16,21,31,45,57,67,87,113,129,145,156,160,168,185,190,218],"graph":[17],"isomorphism":[18],"problem,":[19],"namely":[20],"color":[22,46,114],"refinement":[23,47,115],"and":[25,40,50,103,110,150,189,210,239],"its":[26],"k-dimensional":[27,186],"generalization":[28],"known":[29],"as":[30],"Weisfeiler-Leman":[32,187],"algorithm.":[33],"We":[34,123,166,198],"prove":[35],"that":[36,132],"two":[37,90,104,157,235],"graphs":[38,105,158,180,205,237],"G":[39,65,238],"H":[41],"are":[42,99,106],"indistinguishable":[43],"if":[49,109,112,126,134,149],"only":[51,111,151],"if,":[52,152],"all":[54,154],"trees":[55,171],"T,":[56],"number":[58,69,162],"Hom(T,G)":[59,247],"of":[60,78,163,177,181,194,206,223],"homomorphisms":[61,178],"from":[62,179],"T":[63,245],"to":[64,86,96,144,172,212,231],"equals":[66],"corresponding":[68],"Hom(T,H)":[70],"H.":[72],"There":[73],"is":[74,226,242],"natural":[76],"system":[77,98,147,214],"linear":[79,146,196],"equations":[80],"whose":[81],"nonnegative":[82,93],"integer":[83],"solutions":[84,95,211],"correspond":[85],"isomorphisms":[88],"between":[89,175],"graphs.":[91],"The":[92],"real":[94,139],"called":[100],"fractional":[101],"isomorphisms,":[102],"fractionally":[107],"isomorphic":[108],"cannot":[117],"distinguish":[118],"them":[119],"(Tinhofer":[120],"1986,":[121],"1991).":[122],"show":[124],"that,":[125],"drop":[128,217],"nonnegativity":[130,219],"constraints,":[131],"is,":[133],"look":[136],"arbitrary":[138],"solutions,":[140],"then":[141],"solution":[143],"exists":[148],"t,":[155],"have":[159],"same":[161],"length-t":[164],"walks.":[165],"lift":[167],"results":[169,225],"an":[173],"equivalence":[174],"numbers":[176],"tree":[182,244],"width":[183,209],"k,":[184],"algorithm,":[188],"level-k":[191],"Sherali-Adams":[192],"relaxation":[193],"our":[195,213,224],"program.":[197],"also":[199],"obtain":[200],"partial":[202],"result":[203],"bounded":[207],"path":[208],"where":[215],"constraints.":[220],"A":[221],"consequence":[222],"quasi-linear":[228],"time":[229],"decide":[232],"whether,":[233],"given":[236],"H,":[240],"there":[241],"=":[248],"Hom(T,H).":[249]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}