{"id":"https://openalex.org/W2793588547","doi":"https://doi.org/10.37236/5418","title":"Upper Bound on the Circular Chromatic Number of the Plane","display_name":"Upper Bound on the Circular Chromatic Number of the Plane","publication_year":2018,"publication_date":"2018-03-02","ids":{"openalex":"https://openalex.org/W2793588547","doi":"https://doi.org/10.37236/5418","mag":"2793588547"},"language":"en","primary_location":{"id":"doi:10.37236/5418","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5418","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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://doi.org/10.37236/5418","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075356637","display_name":"Konstanty Junosza-Szaniawski","orcid":"https://orcid.org/0000-0003-0352-8583"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Konstanty Junosza-Szaniawski","raw_affiliation_strings":["Warsaw University of Technology, Faculty of Mathematics and Information Science"],"affiliations":[{"raw_affiliation_string":"Warsaw University of Technology, Faculty of Mathematics and Information Science","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075356637"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":null,"apc_paid":null,"fwci":0.3794,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55624952,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.989799976348877,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.989799976348877,"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"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9628999829292297,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9545000195503235,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8354544043540955},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8277047276496887},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7951064705848694},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6595646739006042},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4642760157585144},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.4367595314979553},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3095950186252594}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8354544043540955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8277047276496887},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7951064705848694},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6595646739006042},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4642760157585144},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.4367595314979553},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3095950186252594}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5418","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5418","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/5418","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5418","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W4256250254","https://openalex.org/W2549201271","https://openalex.org/W1506630056","https://openalex.org/W4238206434","https://openalex.org/W2897501241","https://openalex.org/W4252675521","https://openalex.org/W187561811"],"abstract_inverted_index":{"We":[0,95],"consider":[1],"circular":[2],"version":[3],"of":[4,44,47,73,87,100],"the":[5,23,71,81,88,101,106,119],"famous":[6],"Nelson-Hadwiger":[7],"problem.":[8],"It":[9,79],"is":[10,80],"know":[11],"that":[12,30,58],"4":[13],"colors":[14,19],"are":[15],"necessary":[16],"and":[17],"7":[18],"suffice":[20],"to":[21,118],"color":[22],"euclidean":[24],"plane":[25,89,102],"in":[26,54,105],"such":[27,55],"a":[28,48,51,56],"way":[29,57],"points":[31,59,114],"at":[32,60,115],"distance":[33,61,116],"one":[34,46,62],"get":[35,63],"different":[36],"colors.":[37],"In":[38,66],"$r$-circular":[39,74,85,98],"coloring":[40,75,86,99],"we":[41,69,109],"assign":[42],"arcs":[43,112],"length":[45],"circle":[49],"with":[50,84,90,103],"perimeter":[52],"$r$":[53,91],"disjoint":[64,111],"arcs.":[65],"this":[67],"paper":[68],"show":[70,97],"existence":[72],"for":[76,113],"$r=4+\\frac{4\\sqrt{3}}{3}\\approx":[77],"6.30$.":[78],"first":[82],"result":[83],"smaller":[92],"than":[93],"7.":[94],"also":[96],"$r&lt;7$":[104],"case":[107],"when":[108],"require":[110],"belonging":[117],"internal":[120],"[0.9327,1.0673].":[121]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
