{"id":"https://openalex.org/W3103475865","doi":"https://doi.org/10.1137/19m1299876","title":"Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees","display_name":"Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3103475865","doi":"https://doi.org/10.1137/19m1299876","mag":"3103475865"},"language":"en","primary_location":{"id":"doi:10.1137/19m1299876","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299876","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036596371","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0003-0155-2002"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Linyuan Lu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100357199","display_name":"Zhiyu Wang","orcid":"https://orcid.org/0000-0003-2604-3108"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhiyu Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036596371"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7269,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.90663232,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"34","issue":"4","first_page":"2346","last_page":"2362"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9912999868392944,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.9239394664764404},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9220527410507202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7745535373687744},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.7559882998466492},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6458254456520081},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6363667845726013},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6053614616394043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46820977330207825},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4370272159576416},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.12386474013328552},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08649426698684692},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.044815659523010254}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.9239394664764404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9220527410507202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7745535373687744},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7559882998466492},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6458254456520081},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6363667845726013},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6053614616394043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46820977330207825},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4370272159576416},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.12386474013328552},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08649426698684692},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.044815659523010254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1299876","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299876","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4016617085","display_name":null,"funder_award_id":"DMS-1600811","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2027060958","https://openalex.org/W2028312736","https://openalex.org/W2033599053","https://openalex.org/W2042706982","https://openalex.org/W2058858486","https://openalex.org/W2067019296","https://openalex.org/W2101857785","https://openalex.org/W2126036367","https://openalex.org/W2139317321","https://openalex.org/W2353770281","https://openalex.org/W2585453630","https://openalex.org/W4245931434"],"related_works":["https://openalex.org/W2616445782","https://openalex.org/W2401813478","https://openalex.org/W2963572511","https://openalex.org/W2353770281","https://openalex.org/W2588096572","https://openalex.org/W2979696626","https://openalex.org/W2784505015","https://openalex.org/W2889201402","https://openalex.org/W4298162909","https://openalex.org/W2973163337"],"abstract_inverted_index":{"An":[0],"edge-colored":[1],"graph":[2],"$G$":[3,11],"is":[4,28],"called":[5],"rainbow":[6,22,45,97],"if":[7],"every":[8],"edge":[9],"of":[10,19,34,39,94,103],"receives":[12],"a":[13],"different":[14],"color.":[15],"The":[16],"anti-Ramsey":[17,92],"number":[18,33,93],"$t$":[20,43,95],"edge-disjoint":[21,44,96],"spanning":[23,46,98],"trees,":[24],"denoted":[25],"by":[26],"$r(n,t)$,":[27],"defined":[29],"as":[30],"the":[31,91],"maximum":[32],"colors":[35],"in":[36],"an":[37],"edge-coloring":[38],"$K_n$":[40],"containing":[41],"no":[42],"trees.":[47],"Jahanbekam":[48],"and":[49,105],"West":[50],"[J.":[51],"Graph":[52],"Theory,":[53],"82":[54],"(2016),":[55],"pp.":[56],"75--89]":[57],"conjectured":[58],"that":[59],"for":[60,100],"any":[61],"fixed":[62],"$t$,":[63],"$r(n,t)=(\\begin{smallmatrix}{n-2}\\\\{2}\\end{smallmatrix})+t$":[64],"whenever":[65],"$n\\geq":[66],"2t+2":[67],"\\geq":[68],"6$.":[69],"In":[70],"this":[71,75,89],"paper,":[72],"we":[73],"prove":[74],"conjecture.":[76],"We":[77],"also":[78],"determine":[79],"$r(n,t)$":[80],"when":[81],"$n":[82],"=":[83],"2t+1$.":[84],"Together":[85],"with":[86],"previous":[87],"results,":[88],"gives":[90],"trees":[99],"all":[101],"values":[102],"$n$":[104],"$t$.":[106]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}