{"id":"https://openalex.org/W2769693038","doi":"https://doi.org/10.1017/s0963548318000561","title":"An asymptotic bound for the strong chromatic number","display_name":"An asymptotic bound for the strong chromatic number","publication_year":2019,"publication_date":"2019-03-15","ids":{"openalex":"https://openalex.org/W2769693038","doi":"https://doi.org/10.1017/s0963548318000561","mag":"2769693038"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548318000561","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548318000561","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/90047FC8683FBB3DB2B0ADB3F68BDE37/S0963548318000561a.pdf/div-class-title-an-asymptotic-bound-for-the-strong-chromatic-number-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/90047FC8683FBB3DB2B0ADB3F68BDE37/S0963548318000561a.pdf/div-class-title-an-asymptotic-bound-for-the-strong-chromatic-number-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022659483","display_name":"Allan Lo","orcid":"https://orcid.org/0000-0001-9767-2863"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Allan Lo","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017215680","display_name":"Nicol\u00e1s Sanhueza\u2010Matamala","orcid":"https://orcid.org/0000-0003-4791-5710"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Nicol\u00e1s Sanhueza-Matamala","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017215680"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":null,"apc_paid":null,"fwci":2.534,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87136929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":"5","first_page":"768","last_page":"776"},"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":0.9923999905586243,"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":0.9923999905586243,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9865000247955322,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9749000072479248,"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":0.8734837770462036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6592123508453369},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6277548670768738},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6177781224250793},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5692295432090759},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5371070504188538},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.4492073953151703},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.43143516778945923},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40058839321136475},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3073152005672455},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0934012234210968}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8734837770462036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6592123508453369},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6277548670768738},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6177781224250793},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5692295432090759},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5371070504188538},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.4492073953151703},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.43143516778945923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40058839321136475},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3073152005672455},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0934012234210968}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548318000561","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548318000561","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/90047FC8683FBB3DB2B0ADB3F68BDE37/S0963548318000561a.pdf/div-class-title-an-asymptotic-bound-for-the-strong-chromatic-number-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.08214","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.08214","pdf_url":"https://arxiv.org/pdf/1711.08214","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:pure.atira.dk:Publications/9b4ab228-a754-47f8-a6d4-329a19e3f918","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9b4ab228-a754-47f8-a6d4-329a19e3f918","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/9b4ab228-a754-47f8-a6d4-329a19e3f918","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lo, A & Sanhueza Matamala, N 2019, 'An asymptotic bound for the strong chromatic number', Combinatorics, Probability and Computing, vol. 28, no. 5, pp. 768-776. https://doi.org/10.1017/S0963548318000561","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/9b4ab228-a754-47f8-a6d4-329a19e3f918","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85063064136&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1017/s0963548318000561","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548318000561","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/90047FC8683FBB3DB2B0ADB3F68BDE37/S0963548318000561a.pdf/div-class-title-an-asymptotic-bound-for-the-strong-chromatic-number-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2022013667","display_name":"A graph theoretical approach for combinatorial designs","funder_award_id":"EP/P002420/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8514069245","display_name":null,"funder_award_id":"EP/P002420/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8719353587","display_name":null,"funder_award_id":"EP/P0","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2769693038.pdf","grobid_xml":"https://content.openalex.org/works/W2769693038.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1583095047","https://openalex.org/W1802644857","https://openalex.org/W1965802316","https://openalex.org/W1987360476","https://openalex.org/W2007955950","https://openalex.org/W2008097118","https://openalex.org/W2029416152","https://openalex.org/W2060705114","https://openalex.org/W2061632191","https://openalex.org/W2069550402","https://openalex.org/W2087518343","https://openalex.org/W2093066443","https://openalex.org/W2099989374","https://openalex.org/W2119305988","https://openalex.org/W2146017177","https://openalex.org/W2160755984","https://openalex.org/W2164680149","https://openalex.org/W2478722229","https://openalex.org/W2481708684","https://openalex.org/W3099622868","https://openalex.org/W3128945688","https://openalex.org/W3144881883","https://openalex.org/W4245876577","https://openalex.org/W6634804374"],"related_works":["https://openalex.org/W2090130267","https://openalex.org/W4298388358","https://openalex.org/W2004791814","https://openalex.org/W1995383828","https://openalex.org/W2391570583","https://openalex.org/W1970462054","https://openalex.org/W2077631478","https://openalex.org/W2151291961","https://openalex.org/W2792739039","https://openalex.org/W4242930043"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"strong":[2],"chromatic":[3],"number":[4,20],"\u03c7":[5,86],"s":[6,87],"(":[7,88],"G":[8,13,33,75,81,89,95],")":[9,82,90],"of":[10,41,45],"a":[11,57],"graph":[12,55,74],"on":[14,76],"n":[15,77],"vertices":[16,31,78],"is":[17,98],"the":[18,23,36,49,53],"least":[19],"r":[21,47,62],"with":[22,38,61,79],"following":[24],"property:":[25],"after":[26],"adding":[27],"$r\\lceil":[28],"n/r\\rceil-n$":[29],"isolated":[30],"to":[32],"and":[34,72],"taking":[35],"union":[37],"any":[39],"collection":[40],"spanning":[42],"disjoint":[43],"copies":[44],"K":[46],"in":[48],"same":[50],"vertex":[51,59],"set,":[52],"resulting":[54],"has":[56],"proper":[58],"colouring":[60],"colours.":[63],"We":[64],"show":[65],"that":[66],"for":[67],"every":[68,73],"c":[69],">":[70],"0":[71],"\u0394(":[80],"\u2265":[83],"cn":[84],",":[85],"\u2264":[91],"(2+":[92],"o":[93],"(1))\u0394(":[94],"),":[96],"which":[97],"asymptotically":[99],"best":[100],"possible.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2020-11-23T00:00:00"}