{"id":"https://openalex.org/W1504968429","doi":"https://doi.org/10.37236/3144","title":"Cores of Vertex Transitive Graphs","display_name":"Cores of Vertex Transitive Graphs","publication_year":2013,"publication_date":"2013-05-31","ids":{"openalex":"https://openalex.org/W1504968429","doi":"https://doi.org/10.37236/3144","mag":"1504968429"},"language":"en","primary_location":{"id":"doi:10.37236/3144","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3144","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p45/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p45/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023984902","display_name":"David E. Roberson","orcid":"https://orcid.org/0000-0002-4463-8095"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"David E. Roberson","raw_affiliation_strings":["University of Waterloo","(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023984902"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":1.7148,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79198206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"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":0.9987000226974487,"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":0.9987000226974487,"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":0.998199999332428,"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":0.9979000091552734,"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/combinatorics","display_name":"Combinatorics","score":0.8427027463912964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7331799268722534},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6417681574821472},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6072981953620911},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4769641160964966},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.41754838824272156},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3540859818458557}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8427027463912964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7331799268722534},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6417681574821472},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6072981953620911},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4769641160964966},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.41754838824272156},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3540859818458557}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3144","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3144","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p45/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3144","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3144","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p45/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1504968429.pdf","grobid_xml":"https://content.openalex.org/works/W1504968429.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1572041907","https://openalex.org/W1997799442","https://openalex.org/W4238591275"],"related_works":["https://openalex.org/W4312527695","https://openalex.org/W2361167282","https://openalex.org/W2091342995","https://openalex.org/W3007067598","https://openalex.org/W1528932152","https://openalex.org/W1963504579","https://openalex.org/W2359420171","https://openalex.org/W3129596138","https://openalex.org/W2244024694","https://openalex.org/W4301046126"],"abstract_inverted_index":{"A":[0],"core":[1,31],"of":[2,29,36,49,59,64,93],"a":[3,7,15,50,62],"graph":[4,53],"X":[5,13],"is":[6],"vertex":[8,24,47,51,74,91,94],"minimal":[9],"subgraph":[10],"to":[11],"which":[12,60],"admits":[14],"homomorphism.":[16],"Hahn":[17],"and":[18,73],"Tardif":[19],"have":[20,108],"shown":[21],"that":[22,69,89],"for":[23],"transitive":[25,52,75,95],"graphs,":[26],"the":[27,30,34,37,41,46,90],"size":[28,35,81,103],"must":[32],"divide":[33],"graph.":[38],"This":[39],"motivates":[40],"following":[42],"question:":[43],"when":[44],"can":[45],"set":[48],"be":[54],"partitioned":[55],"into":[56],"sets":[57,92],"each":[58],"induce":[61],"copy":[63],"its":[65],"core?":[66],"We":[67,86],"show":[68,88],"normal":[70],"Cayley":[71],"graphs":[72,76,96],"with":[77,97],"cores":[78,98],"half":[79,101],"their":[80,102],"always":[82],"admit":[83],"such":[84,109],"partitions.":[85,110],"also":[87],"less":[99],"than":[100],"do":[104],"not,":[105],"in":[106],"general,":[107]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
