{"id":"https://openalex.org/W7201849587","doi":"https://doi.org/10.48550/arxiv.2608.06254","title":"Minimal Cayley graphs with large chromatic number","display_name":"Minimal Cayley graphs with large chromatic number","publication_year":2026,"publication_date":"2026-08-06","ids":{"openalex":"https://openalex.org/W7201849587","doi":"https://doi.org/10.48550/arxiv.2608.06254"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.06254","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06254","pdf_url":"https://arxiv.org/pdf/2608.06254","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/2608.06254","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144373768","display_name":"James Davies","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Davies, James","raw_affiliation_strings":["Leipzig University , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Leipzig University , Germany,","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012019509","display_name":"Meike Hatzel","orcid":"https://orcid.org/0000-0003-3249-1169","observed_orcids":["https://orcid.org/0000-0003-3249-1169"]},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hatzel, Meike","raw_affiliation_strings":["TU Darmstadt , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Darmstadt , Germany,","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066277903","display_name":"Liana Yepremyan","orcid":"https://orcid.org/0000-0001-7277-4273","observed_orcids":["https://orcid.org/0000-0001-7277-4273"]},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yepremyan, Liana","raw_affiliation_strings":["Department of Mathematics , Emory University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Emory University ,","institution_ids":["https://openalex.org/I150468666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10849","display_name":"Finite Group Theory Research","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.0013000000035390258,"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":0.0006000000284984708,"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/chromatic-number","display_name":"chromatic number","score":0.9179999828338623},{"id":"https://openalex.org/keywords/cayley-graphs","display_name":"Cayley graphs","score":0.7820000052452087},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"graph coloring","score":0.5490000247955322},{"id":"https://openalex.org/keywords/finite-groups","display_name":"finite groups","score":0.5059999823570251}],"concepts":[{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.828499972820282},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7080000042915344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6689000129699707},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5447999835014343},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42100000381469727},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.36559998989105225},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.3249000012874603},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C18586221","wikidata":"https://www.wikidata.org/wiki/Q2778065","display_name":"Cayley transform","level":5,"score":0.275299996137619},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C4093544","wikidata":"https://www.wikidata.org/wiki/Q179208","display_name":"Cayley's theorem","level":5,"score":0.2606000006198883},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25870001316070557}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.06254","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06254","pdf_url":"https://arxiv.org/pdf/2608.06254","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.2608.06254","doi":"https://doi.org/10.48550/arxiv.2608.06254","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.06254","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.06254","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06254","pdf_url":"https://arxiv.org/pdf/2608.06254","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/G1020685157","display_name":"Forbidden and Colored Subgraphs","funder_award_id":"2247013","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7201849587.pdf","grobid_xml":"https://content.openalex.org/works/W7201849587.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4225476106","https://openalex.org/W4403324143","https://openalex.org/W4407035883","https://openalex.org/W4416971463","https://openalex.org/W7171818793"],"related_works":["https://openalex.org/W7171818793","https://openalex.org/W4405567348","https://openalex.org/W6922487376","https://openalex.org/W2135869299","https://openalex.org/W2069660130","https://openalex.org/W4403324143","https://openalex.org/W2562382333","https://openalex.org/W3108706109","https://openalex.org/W2249539576","https://openalex.org/W1967114635"],"abstract_inverted_index":{"Resolving":[0],"Babai's":[1],"minimal":[2,9],"Cayley":[3,10],"graph":[4],"problem,":[5],"we":[6],"construct":[7],"finite":[8],"graphs":[11],"with":[12],"arbitrarily":[13],"large":[14],"chromatic":[15],"number.":[16]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-08T00:00:00"}