{"id":"https://openalex.org/W1555822721","doi":"https://doi.org/10.37236/177","title":"Bounds on the Distinguishing Chromatic Number","display_name":"Bounds on the Distinguishing Chromatic Number","publication_year":2009,"publication_date":"2009-07-24","ids":{"openalex":"https://openalex.org/W1555822721","doi":"https://doi.org/10.37236/177","mag":"1555822721"},"language":"en","primary_location":{"id":"doi:10.37236/177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r88/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/v16i1r88/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047310888","display_name":"Karen L. Collins","orcid":"https://orcid.org/0000-0002-3799-1157"},"institutions":[{"id":"https://openalex.org/I100538780","display_name":"Wesleyan University","ror":"https://ror.org/05h7xva58","country_code":"US","type":"education","lineage":["https://openalex.org/I100538780"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Karen L. Collins","raw_affiliation_strings":["Wesleyan Univ"],"affiliations":[{"raw_affiliation_string":"Wesleyan Univ","institution_ids":["https://openalex.org/I100538780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016204885","display_name":"Mark Hovey","orcid":null},"institutions":[{"id":"https://openalex.org/I100538780","display_name":"Wesleyan University","ror":"https://ror.org/05h7xva58","country_code":"US","type":"education","lineage":["https://openalex.org/I100538780"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark Hovey","raw_affiliation_strings":["Wesleyan Univ"],"affiliations":[{"raw_affiliation_string":"Wesleyan Univ","institution_ids":["https://openalex.org/I100538780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089382229","display_name":"Ann N. Trenk","orcid":"https://orcid.org/0000-0003-1145-3489"},"institutions":[{"id":"https://openalex.org/I189731429","display_name":"Wellesley College","ror":"https://ror.org/01srpnj69","country_code":"US","type":"education","lineage":["https://openalex.org/I189731429"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ann N. Trenk","raw_affiliation_strings":["WELLESLEY College"],"affiliations":[{"raw_affiliation_string":"WELLESLEY College","institution_ids":["https://openalex.org/I189731429"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047310888"],"corresponding_institution_ids":["https://openalex.org/I100538780"],"apc_list":null,"apc_paid":null,"fwci":0.3535,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.58677781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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/combinatorics","display_name":"Combinatorics","score":0.8822798728942871},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8499330282211304},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6969913244247437},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6470800638198853},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5373199582099915},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4226140081882477}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8822798728942871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8499330282211304},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6969913244247437},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6470800638198853},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5373199582099915},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4226140081882477}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r88/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.178.4380","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4380","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://claude.math.wesleyan.edu/%7Emhovey/papers/collins-trenk.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.3727","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.3727","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r88.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r88/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":[{"id":"https://openalex.org/F4320308518","display_name":"Wellesley College","ror":"https://ror.org/01srpnj69"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1555822721.pdf","grobid_xml":"https://content.openalex.org/works/W1555822721.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W240203132","https://openalex.org/W1516924510","https://openalex.org/W1620207187","https://openalex.org/W1855706715","https://openalex.org/W1972858392","https://openalex.org/W1999060257","https://openalex.org/W2000073029","https://openalex.org/W2015059258","https://openalex.org/W2057735049","https://openalex.org/W2105903417","https://openalex.org/W2154008353","https://openalex.org/W2169476811","https://openalex.org/W2187787310","https://openalex.org/W2316759756","https://openalex.org/W3043060850","https://openalex.org/W6627421581","https://openalex.org/W6631511135"],"related_works":["https://openalex.org/W4287819550","https://openalex.org/W1964998024","https://openalex.org/W2369184155","https://openalex.org/W2125677183","https://openalex.org/W2000924970","https://openalex.org/W2067133893","https://openalex.org/W2287003313","https://openalex.org/W2032656190","https://openalex.org/W1972748334","https://openalex.org/W2072754781"],"abstract_inverted_index":{"Collins":[0],"and":[1,81,112,119,154],"Trenk":[2],"define":[3],"the":[4,15,24,30,39,48,62,77,134],"distinguishing":[5],"chromatic":[6,78],"number":[7,17,79],"$\\chi_D(G)$":[8,45,60,73],"of":[9,18,26,33,65,76,95,148],"a":[10,117],"graph":[11,50],"$G$":[12,27,34],"to":[13,21,61],"be":[14],"minimum":[16],"colors":[19,37],"needed":[20],"properly":[22],"color":[23],"vertices":[25],"so":[28],"that":[29,35,58,83],"only":[31],"automorphism":[32,63,146],"preserves":[36],"is":[38,86,91,116],"identity.":[40],"They":[41],"prove":[42,56,68],"results":[43,57,157],"about":[44],"based":[46],"on":[47],"underlying":[49],"$G$.":[51,66],"In":[52,142],"this":[53],"paper":[54],"we":[55,132,144],"relate":[59],"group":[64,94,121],"We":[67],"two":[69],"upper":[70],"bounds":[71],"for":[72,158],"in":[74],"terms":[75],"$\\chi(G)$":[80],"show":[82],"each":[84],"result":[85],"tight:":[87],"(1)":[88],"if":[89,114],"Aut$(G)$":[90,115],"any":[92],"finite":[93,118],"order":[96],"$p_1^{i_1}":[97],"p_2^{i_2}":[98],"\\cdots":[99,109,127],"p_k^{i_k}$":[100],"then":[101,131],"$\\chi_D(G)":[102,137,151],"\\le":[103,138],"\\chi(G)":[104,139],"+":[105,107,110,140],"i_1":[106],"i_2":[108],"i_k$,":[111],"(2)":[113],"abelian":[120],"written":[122],"Aut$(G)":[123],"=":[124,152],"{\\Bbb":[125,129],"Z}_{p_{1}^{i_{1}}}\\times":[126],"\\times":[128],"Z}_{p_{k}^{i_{k}}}$":[130],"get":[133],"improved":[135],"bound":[136],"k$.":[141],"addition,":[143],"characterize":[145],"groups":[147],"graphs":[149,159],"with":[150,160],"2$":[153],"discuss":[155],"similar":[156],"$\\chi_D(G)=3$.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}