{"id":"https://openalex.org/W2045583023","doi":"https://doi.org/10.1007/bf02122553","title":"On multiplicative graphs and the product conjecture","display_name":"On multiplicative graphs and the product conjecture","publication_year":1988,"publication_date":"1988-03-01","ids":{"openalex":"https://openalex.org/W2045583023","doi":"https://doi.org/10.1007/bf02122553","mag":"2045583023"},"language":"en","primary_location":{"id":"doi:10.1007/bf02122553","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02122553","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5015310429","display_name":"Roland H\u00e4ggkvist","orcid":null},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"R. H\u00e4ggkvist","raw_affiliation_strings":["University of Stockholm, Stockholm, Sweden","University of Stockholm, Stockholm, #N#Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Stockholm, Stockholm, Sweden","institution_ids":["https://openalex.org/I161593684"]},{"raw_affiliation_string":"University of Stockholm, Stockholm, #N#Sweden","institution_ids":["https://openalex.org/I161593684"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075416144","display_name":"Pavol Hell","orcid":"https://orcid.org/0000-0001-7609-9746"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. Hell","raw_affiliation_strings":["Simon Fraser University, Burnaby, B. C., USA","Simon Fraser University, Burnaby, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, B. C., USA","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Simon Fraser University, Burnaby, USA","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069689068","display_name":"Donald J. Miller","orcid":null},"institutions":[{"id":"https://openalex.org/I173388201","display_name":"Texas A&M University-Victoria","ror":"https://ror.org/01khwek78","country_code":"US","type":"education","lineage":["https://openalex.org/I173388201"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. J. Miller","raw_affiliation_strings":["University of Victoria, Victoria, B. C., USA","University of Victoria, Victoria, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Victoria, Victoria, B. C., USA","institution_ids":["https://openalex.org/I173388201"]},{"raw_affiliation_string":"University of Victoria, Victoria, USA","institution_ids":["https://openalex.org/I173388201"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060006240","display_name":"V\u00edctor Neumann Lara","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120382","display_name":"Universidad de las Am\u00e9ricas","ror":"https://ror.org/02j003371","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210120382"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"V. Neumann Lara","raw_affiliation_strings":["University of Mexico, Mexico City, Mexico","University of Mexico Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Mexico, Mexico City, Mexico","institution_ids":["https://openalex.org/I4210120382"]},{"raw_affiliation_string":"University of Mexico Mexico City, Mexico","institution_ids":["https://openalex.org/I4210120382"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.9048,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.98273572,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"8","issue":"1","first_page":"63","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"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":0.9908000230789185,"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":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8531734943389893},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8063992261886597},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6805768013000488},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6502519249916077},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5264806747436523},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.5214332938194275},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.511723518371582},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.501258373260498},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47488993406295776},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4378221035003662},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2664076089859009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07960760593414307}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8531734943389893},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8063992261886597},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6805768013000488},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6502519249916077},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5264806747436523},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.5214332938194275},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.511723518371582},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.501258373260498},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47488993406295776},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4378221035003662},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2664076089859009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07960760593414307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02122553","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02122553","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/1589","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/1589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"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":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W315200476","https://openalex.org/W1544755278","https://openalex.org/W1559046348","https://openalex.org/W2004142016","https://openalex.org/W2019992994","https://openalex.org/W2044272852","https://openalex.org/W2048118184","https://openalex.org/W2069527258","https://openalex.org/W2077801899","https://openalex.org/W2095076239","https://openalex.org/W2125850735","https://openalex.org/W2134331399","https://openalex.org/W2167519573","https://openalex.org/W2188797527","https://openalex.org/W2315063369","https://openalex.org/W2326118140","https://openalex.org/W2799004609","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W4308159138","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W4327811209","https://openalex.org/W3037616202","https://openalex.org/W2157313229","https://openalex.org/W2582753012","https://openalex.org/W4300101497","https://openalex.org/W2038260770","https://openalex.org/W2058751658"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}