{"id":"https://openalex.org/W2523851198","doi":"https://doi.org/10.37236/5663","title":"On the Multi-Colored Ramsey Numbers of Paths and Even Cycles","display_name":"On the Multi-Colored Ramsey Numbers of Paths and Even Cycles","publication_year":2016,"publication_date":"2016-09-30","ids":{"openalex":"https://openalex.org/W2523851198","doi":"https://doi.org/10.37236/5663","mag":"2523851198"},"language":"en","primary_location":{"id":"doi:10.37236/5663","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5663","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/10.37236/5663","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087999366","display_name":"G\u00e1bor N. S\u00e1rk\u00f6zy","orcid":null},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G\u00e1bor N. S\u00e1rk\u00f6zy","raw_affiliation_strings":["Worcester Polytechnic Institute"],"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087999366"],"corresponding_institution_ids":["https://openalex.org/I107077323"],"apc_list":null,"apc_paid":null,"fwci":7.5516,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.9766939,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"3","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":0.9998999834060669,"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":0.9998999834060669,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9957000017166138,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9889000058174133,"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":0.8866525888442993},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.8357027173042297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.828386664390564},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5593311786651611},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.4757663607597351},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.42368900775909424},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.0995418131351471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06841889023780823},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04751905798912048}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8866525888442993},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.8357027173042297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.828386664390564},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5593311786651611},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.4757663607597351},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.42368900775909424},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0995418131351471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06841889023780823},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04751905798912048},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5663","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5663","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"},{"id":"pmh:oai:real.mtak.hu:43729","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/5663","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5663","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1604945782","https://openalex.org/W1990486130","https://openalex.org/W1996106086","https://openalex.org/W2031273169","https://openalex.org/W2067223116","https://openalex.org/W2083899663","https://openalex.org/W2090747987","https://openalex.org/W2095689360","https://openalex.org/W2138513955","https://openalex.org/W2275005719"],"related_works":["https://openalex.org/W13791998","https://openalex.org/W2046202915","https://openalex.org/W2101126588","https://openalex.org/W2474561564","https://openalex.org/W2134378549","https://openalex.org/W2949231378","https://openalex.org/W4301914467","https://openalex.org/W1561903201","https://openalex.org/W2127133075","https://openalex.org/W3080236997"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,20,37,54],"improve":[4],"the":[5,9,22,78],"upper":[6],"bound":[7],"on":[8],"multi-color":[10],"Ramsey":[11],"numbers":[12],"of":[13,77,84],"paths":[14],"and":[15,51],"even":[16,52],"cycles.":[17],"More":[18],"precisely,":[19],"prove":[21],"following.":[23],"For":[24,47],"every":[25,48],"$r\\geq":[26,49],"2$":[27,50],"there":[28],"exists":[29],"an":[30],"$n_0=n_0(r)$":[31],"such":[32],"that":[33,81],"for":[34],"$n\\geq":[35],"n_0$":[36],"have":[38,55],"$$R_r(P_n)":[39],"\\leq":[40,57],"\\left(":[41,58],"r":[42,59],"-":[43,60],"\\frac{r}{16r^3+1}":[44,61],"\\right)":[45,62],"n.$$":[46],"$n$":[53],"$$R_r(C_n)":[56],"n":[63],"+":[64],"o(n)":[65],"\\text{":[66],"as":[67],"}n\\rightarrow":[68],"\\infty.$$":[69],"The":[70],"main":[71],"tool":[72],"is":[73],"a":[74],"stability":[75],"version":[76],"Erd\u0151s-Gallai":[79],"theorem":[80],"may":[82],"be":[83],"independent":[85],"interest.":[86]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
