{"id":"https://openalex.org/W2110591747","doi":"https://doi.org/10.37236/1131","title":"On Lengths of Rainbow Cycles","display_name":"On Lengths of Rainbow Cycles","publication_year":2006,"publication_date":"2006-11-17","ids":{"openalex":"https://openalex.org/W2110591747","doi":"https://doi.org/10.37236/1131","mag":"2110591747"},"language":"en","primary_location":{"id":"doi:10.37236/1131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r105/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/v13i1r105/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017038708","display_name":"Boris V. Alexeev","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Boris Alexeev","raw_affiliation_strings":["Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017038708"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.8921,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84884211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"1","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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9900000095367432,"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/rainbow","display_name":"Rainbow","score":0.9873606562614441},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7584924697875977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6997799873352051},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.6473979949951172},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.47002291679382324},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.4101375937461853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15032225847244263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13514509797096252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07897752523422241},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06714347004890442},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.0550864040851593}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.9873606562614441},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7584924697875977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6997799873352051},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.6473979949951172},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.47002291679382324},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4101375937461853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15032225847244263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13514509797096252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07897752523422241},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06714347004890442},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0550864040851593},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r105/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:10.1.1.236.5959","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.5959","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0507456v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.8674","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.8674","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0507456v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.1004","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.1004","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r105.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r105/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/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2110591747.pdf","grobid_xml":"https://content.openalex.org/works/W2110591747.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W254482520","https://openalex.org/W2028312736","https://openalex.org/W2034225398","https://openalex.org/W2036460087","https://openalex.org/W2062513475","https://openalex.org/W2083869960","https://openalex.org/W2114211390","https://openalex.org/W6600126919","https://openalex.org/W6628667382"],"related_works":["https://openalex.org/W2394414377","https://openalex.org/W2386551956","https://openalex.org/W2945204557","https://openalex.org/W1989888546","https://openalex.org/W2797212079","https://openalex.org/W2725202876","https://openalex.org/W1984408232","https://openalex.org/W2949720779","https://openalex.org/W2591829030","https://openalex.org/W2033759535"],"abstract_inverted_index":{"We":[0,21],"prove":[1],"several":[2,90],"results":[3],"regarding":[4],"edge-colored":[5],"complete":[6],"graphs":[7],"and":[8,29],"rainbow":[9,42,58],"cycles,":[10],"cycles":[11],"with":[12],"no":[13],"color":[14],"appearing":[15],"on":[16],"more":[17],"than":[18,67],"one":[19],"edge.":[20],"settle":[22],"a":[23,36,41,57,78],"question":[24],"posed":[25],"by":[26,31],"Ball,":[27],"Pultr":[28],"Vojt\u011bchovsk\u00fd":[30],"showing":[32],"that":[33,77],"if":[34],"such":[35],"coloring":[37],"does":[38,54,81],"not":[39,55,82],"contain":[40,56],"cycle":[43,59],"of":[44,60],"length":[45,61],"$n$,":[46],"where":[47],"$n$":[48],"is":[49],"odd,":[50],"then":[51],"it":[52],"also":[53],"$m$":[62,65],"for":[63,84],"all":[64],"greater":[66],"$2n^2$.":[68],"In":[69],"addition,":[70],"we":[71,88],"present":[72],"two":[73],"examples":[74],"which":[75],"demonstrate":[76],"similar":[79],"result":[80],"hold":[83],"even":[85],"$n$.":[86],"Finally,":[87],"state":[89],"open":[91],"problems":[92],"in":[93],"the":[94],"area.":[95]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
