{"id":"https://openalex.org/W7221030908","doi":"https://doi.org/10.48550/arxiv.2610.07927","title":"Topological and Geometric Perspectives on Homomorphism Indistinguishability","display_name":"Topological and Geometric Perspectives on Homomorphism Indistinguishability","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7221030908","doi":"https://doi.org/10.48550/arxiv.2610.07927"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07927","pdf_url":"https://arxiv.org/pdf/2610.07927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.07927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059060171","display_name":"Josse van Dobben de Bruyn","orcid":"https://orcid.org/0000-0002-8996-9824","observed_orcids":["https://orcid.org/0000-0002-8996-9824"]},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"de Bruyn, Josse van Dobben","raw_affiliation_strings":["Charles University , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles University , Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077654858","display_name":"J\u00e9r\u00e9mie Marqu\u00e8s","orcid":"https://orcid.org/0000-0001-9457-7465","observed_orcids":["https://orcid.org/0000-0001-9457-7465"]},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marqu\u00e8s, J\u00e9r\u00e9mie","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d'Azur , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur , France","institution_ids":["https://openalex.org/I201841394"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023984902","display_name":"David E. Roberson","orcid":"https://orcid.org/0000-0002-4463-8095","observed_orcids":["https://orcid.org/0000-0002-4463-8095"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Roberson, David E.","raw_affiliation_strings":["Technical University of Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086010577","display_name":"Tim Seppelt","orcid":"https://orcid.org/0000-0002-6447-0568","observed_orcids":["https://orcid.org/0000-0002-6447-0568"]},"institutions":[{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Seppelt, Tim","raw_affiliation_strings":["IT-Universitetet i K\u00f8benhavn , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT-Universitetet i K\u00f8benhavn , Denmark","institution_ids":["https://openalex.org/I83467386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130650919","display_name":"Gian Luca Spitzer","orcid":"https://orcid.org/0009-0008-0270-506X","observed_orcids":["https://orcid.org/0009-0008-0270-506X"]},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Spitzer, Gian Luca","raw_affiliation_strings":["Universit\u00e9 de Bordeaux , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bordeaux , France","institution_ids":["https://openalex.org/I15057530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013404440","display_name":"Peter Zeman","orcid":"https://orcid.org/0000-0003-0071-9149","observed_orcids":["https://orcid.org/0000-0003-0071-9149"]},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Zeman, Peter","raw_affiliation_strings":["Charles University , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles University , Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.961899995803833,"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":0.961899995803833,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.008700000122189522,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.007400000002235174,"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/graph-isomorphism","display_name":"graph isomorphism","score":0.8209999799728394},{"id":"https://openalex.org/keywords/graph-homomorphisms","display_name":"graph homomorphisms","score":0.8040000200271606},{"id":"https://openalex.org/keywords/axiomatization","display_name":"axiomatization","score":0.9039999842643738},{"id":"https://openalex.org/keywords/graph-invariants","display_name":"graph invariants","score":0.609000027179718},{"id":"https://openalex.org/keywords/graph-reconstruction","display_name":"graph reconstruction","score":0.625},{"id":"https://openalex.org/keywords/graph-classes","display_name":"graph classes","score":0.40299999713897705}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.9272000193595886},{"id":"https://openalex.org/C7036158","wikidata":"https://www.wikidata.org/wiki/Q3385162","display_name":"Graph homomorphism","level":5,"score":0.7287999987602234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6583999991416931},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6431000232696533},{"id":"https://openalex.org/C175316100","wikidata":"https://www.wikidata.org/wiki/Q3882299","display_name":"Algebra homomorphism","level":3,"score":0.6121000051498413},{"id":"https://openalex.org/C26231708","wikidata":"https://www.wikidata.org/wiki/Q1065966","display_name":"Isomorphism theorem","level":2,"score":0.5424000024795532},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.5115000009536743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5099999904632568},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5067999958992004},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48579999804496765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4837000072002411},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.4099000096321106},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.3650999963283539},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.2937000095844269},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07927","pdf_url":"https://arxiv.org/pdf/2610.07927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.07927","doi":"https://doi.org/10.48550/arxiv.2610.07927","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07927","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07927","pdf_url":"https://arxiv.org/pdf/2610.07927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1304993860","display_name":null,"funder_award_id":"101071674","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G168130044","display_name":"Institut Mittag-Leffler","funder_award_id":"2021-06594","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G199127864","display_name":null,"funder_award_id":"670624","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5246331465","display_name":null,"funder_award_id":"101077083","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221030908.pdf","grobid_xml":"https://content.openalex.org/works/W7221030908.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W273178449","https://openalex.org/W2004030389","https://openalex.org/W2014987816","https://openalex.org/W2033026830","https://openalex.org/W2058341099","https://openalex.org/W2100355951","https://openalex.org/W2104417474","https://openalex.org/W2141382791","https://openalex.org/W2236332462","https://openalex.org/W2272406345","https://openalex.org/W2490805901","https://openalex.org/W2524594508","https://openalex.org/W2559678959","https://openalex.org/W2610844084","https://openalex.org/W2810794926","https://openalex.org/W2907423062","https://openalex.org/W2962810718","https://openalex.org/W3093996209","https://openalex.org/W3107179006","https://openalex.org/W3163906208","https://openalex.org/W3176983719","https://openalex.org/W4282550487","https://openalex.org/W4286599505","https://openalex.org/W4397009053","https://openalex.org/W4399198598","https://openalex.org/W4399418281","https://openalex.org/W4400716687","https://openalex.org/W4402404669","https://openalex.org/W4407333211","https://openalex.org/W4413786438","https://openalex.org/W4414770562","https://openalex.org/W6906822436","https://openalex.org/W6910501128","https://openalex.org/W6925671983","https://openalex.org/W6963100883","https://openalex.org/W7079985207","https://openalex.org/W7084574019","https://openalex.org/W7128530339","https://openalex.org/W7167626371","https://openalex.org/W7170343169","https://openalex.org/W7203494026","https://openalex.org/W7220436653"],"related_works":["https://openalex.org/W7167814244","https://openalex.org/W6925671983","https://openalex.org/W7170343169","https://openalex.org/W6963100883","https://openalex.org/W4321649496","https://openalex.org/W7128530339","https://openalex.org/W2970918966","https://openalex.org/W4317832152","https://openalex.org/W7097875299","https://openalex.org/W6944668487"],"abstract_inverted_index":{"Two":[0],"graphs":[1,49],"$G$":[2,27],"and":[3,53,107,159],"$H$":[4],"are":[5,50,57],"homomorphism":[6,58,64,101,112,157],"indistinguishable":[7,59],"over":[8,60],"a":[9,68,121,125,142],"graph":[10,16,73,80,129,138],"class":[11],"$\\mathcal{F}$":[12],"if,":[13,52,55],"for":[14,96,136,162],"every":[15],"$F":[17],"\\in":[18],"\\mathcal{F}$,":[19],"the":[20,31,84,132,154,163],"number":[21,32],"of":[22,33,67,71,86,100,128,131,145,156],"homomorphisms":[23,34],"from":[24,35],"$F$":[25,36,139],"to":[26,30,37,141],"is":[28,124],"equal":[29],"$H$.":[38],"Lov\u00e1sz":[39,146],"(Acta":[40],"Mathematica":[41],"Academiae":[42],"Scientiarum":[43],"Hungarica,":[44],"1967)":[45],"showed":[46],"that":[47],"two":[48],"isomorphic":[51],"only":[54],"they":[56],"all":[61],"graphs.":[62],"Subsequently,":[63],"indistinguishability":[65,102,158],"relations":[66],"long":[69],"list":[70],"natural":[72,79],"classes":[74],"have":[75],"been":[76],"equated":[77],"with":[78,111],"isomorphism":[81],"relaxations.":[82],"Given":[83],"wealth":[85],"such":[87,116],"results,":[88],"Atserias,":[89],"Kolaitis,":[90],"&":[91,147],"Wu":[92],"(LICS":[93],"2021)":[94],"asked":[95],"an":[97,117],"axiomatic":[98,118],"characterisation":[99,127],"relations.":[103],"By":[104],"exhibiting":[105],"topological":[106],"geometric":[108],"structure":[109],"associated":[110],"indistinguishability,":[113],"we":[114,152],"derive":[115],"characterisation.":[119],"Here,":[120],"central":[122],"ingredient":[123],"novel":[126],"parameters":[130],"form":[133],"$\\hom(F,":[134],"\\star)$":[135],"some":[137],"alternative":[140],"previous":[143],"result":[144],"Schrijver":[148],"(JCTA":[149],"2010).":[150],"Moreover,":[151],"investigate":[153],"topology":[155],"discuss":[160],"repercussions":[161],"Ulam--Kelly":[164],"Reconstruction":[165],"Conjecture.":[166]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
