{"id":"https://openalex.org/W2269072799","doi":"https://doi.org/10.1137/15m1035422","title":"Coloring Powers and Girth","display_name":"Coloring Powers and Girth","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2269072799","doi":"https://doi.org/10.1137/15m1035422","mag":"2269072799"},"language":"en","primary_location":{"id":"doi:10.1137/15m1035422","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1035422","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.08826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019911064","display_name":"Ross J. Kang","orcid":"https://orcid.org/0000-0002-4219-593X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ross J. Kang","raw_affiliation_strings":["IMAPP - Institute for Mathematics, Astrophysics and Particle Physics (P.O. Box 9010,  6500 GL Nijmegen - Pays-Bas)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMAPP - Institute for Mathematics, Astrophysics and Particle Physics (P.O. Box 9010,  6500 GL Nijmegen - Pays-Bas)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047120459","display_name":"Fran\u00e7ois Pirot","orcid":"https://orcid.org/0000-0002-1392-9623"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Pirot","raw_affiliation_strings":["ORPAILLEUR - Knowledge  representation, reasonning (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ORPAILLEUR - Knowledge  representation, reasonning (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.164,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.73765158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"4","first_page":"1938","last_page":"1949"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.8931561708450317},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8071585893630981},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6543718576431274},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6092628836631775},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6079473495483398},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5592265725135803},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5056717395782471}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8931561708450317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8071585893630981},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6543718576431274},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6092628836631775},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6079473495483398},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5592265725135803},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5056717395782471},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1035422","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1035422","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.08826","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.08826","pdf_url":"https://arxiv.org/pdf/1511.08826","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,"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":"pmh:oai:HAL:hal-03007196v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03007196","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Discrete Mathematics, 2016, 30 (4), pp.1938 - 1949. ⟨10.1137/15m1035422⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/161274","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/161274","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Siam Journal on Discrete Mathematics, 30, 4, pp. 1938-1949","raw_type":"Article / Letter to editor"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.08826","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.08826","pdf_url":"https://arxiv.org/pdf/1511.08826","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,"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":[{"display_name":"Sustainable cities and communities","score":0.7699999809265137,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1984697505","https://openalex.org/W1985549462","https://openalex.org/W1996106086","https://openalex.org/W2018074536","https://openalex.org/W2040452405","https://openalex.org/W2048800330","https://openalex.org/W2058462653","https://openalex.org/W2167763892","https://openalex.org/W2167990241","https://openalex.org/W3106206962","https://openalex.org/W4241138392"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2311783135","https://openalex.org/W2903806635","https://openalex.org/W4353100660","https://openalex.org/W3194346534","https://openalex.org/W1902769386","https://openalex.org/W1501751563","https://openalex.org/W4296243762","https://openalex.org/W2158905189","https://openalex.org/W4319874546"],"abstract_inverted_index":{"Alon":[0],"and":[1,18,47],"Mohar":[2],"(2002)":[3],"posed":[4],"the":[5,25,31,35,73,77],"following":[6],"problem:":[7],"among":[8],"all":[9,53],"graphs":[10],"$G$":[11],"of":[12,29,34,38,54],"maximum":[13],"degree":[14],"at":[15,20],"most":[16],"$d$":[17],"girth":[19],"least":[21],"$g$,":[22],"what":[23],"is":[24],"largest":[26],"possible":[27],"value":[28],"$\\chi(G^t)$,":[30],"chromatic":[32],"number":[33],"$t$th":[36],"power":[37],"$G$?":[39],"For":[40],"$t\\ge":[41],"3$,":[42],"we":[43],"provide":[44],"several":[45],"upper":[46,67],"lower":[48,78],"bounds":[49,68,79],"concerning":[50],"this":[51],"problem,":[52],"which":[55],"are":[56,80,87],"sharp":[57],"up":[58],"to":[59],"a":[60],"constant":[61],"factor":[62],"as":[63],"$d\\to":[64],"\\infty$.":[65],"The":[66],"rely":[69],"in":[70],"part":[71],"on":[72],"probabilistic":[74],"method,":[75],"while":[76],"various":[81],"direct":[82],"constructions":[83],"whose":[84],"building":[85],"blocks":[86],"incidence":[88],"structures.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}