{"id":"https://openalex.org/W2108308667","doi":"https://doi.org/10.37236/660","title":"Trees with an On-Line Degree Ramsey Number of Four","display_name":"Trees with an On-Line Degree Ramsey Number of Four","publication_year":2011,"publication_date":"2011-09-02","ids":{"openalex":"https://openalex.org/W2108308667","doi":"https://doi.org/10.37236/660","mag":"2108308667"},"language":"en","primary_location":{"id":"doi:10.37236/660","is_oa":true,"landing_page_url":"https://doi.org/10.37236/660","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p173/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/v18i1p173/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056513353","display_name":"David Rolnick","orcid":"https://orcid.org/0000-0002-2855-393X"},"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":"David Rolnick","raw_affiliation_strings":["Massachusetts Institute of Technology Cambridge, MA, USA","Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056513353"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.4476,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61603244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9926999807357788,"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":0.8274651765823364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.610553503036499},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5778969526290894},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4770057499408722},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.45849549770355225},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4555460512638092}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8274651765823364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.610553503036499},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5778969526290894},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4770057499408722},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45849549770355225},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4555460512638092},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/660","is_oa":true,"landing_page_url":"https://doi.org/10.37236/660","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p173/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:10.1.1.1023.2799","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1023.2799","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dspace.mit.edu/bitstream/handle/1721.1/89807/Rolnick-2011-Trees%20with%20an%20on-line.pdf%3Bjsessionid%3DE19F076DE75CCDEE791512B586B6EA90?sequence%3D1","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.5972","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.5972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p173/pdf/","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/89807","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/89807","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.37236/660","is_oa":true,"landing_page_url":"https://doi.org/10.37236/660","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p173/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":[{"id":"https://metadata.un.org/sdg/11","score":0.6700000166893005,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G7587565994","display_name":"REU Site: An undergraduate research program in Discrete Mathematics","funder_award_id":"0754106","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7767944625","display_name":null,"funder_award_id":"H98230-06-1-0013","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G7845798442","display_name":null,"funder_award_id":"H98230","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320311500","display_name":"University of Minnesota Duluth","ror":"https://ror.org/01hy4qx27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108308667.pdf","grobid_xml":"https://content.openalex.org/works/W2108308667.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1524397983","https://openalex.org/W2060194042"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1596176126","https://openalex.org/W2362020254","https://openalex.org/W4385659976","https://openalex.org/W1984128946","https://openalex.org/W1971379739","https://openalex.org/W3163567768"],"abstract_inverted_index":{"On-line":[0],"Ramsey":[1,93],"theory":[2],"studies":[3],"a":[4,18,54,58,97,130],"graph-building":[5],"game":[6],"between":[7],"two":[8],"players.":[9],"The":[10,36,90],"player":[11,22],"called":[12,23,40],"Builder":[13,106],"builds":[14],"edges":[15],"one":[16],"at":[17],"time,":[19],"and":[20,62],"the":[21,41,49,70,74,77,101,114],"Painter":[24],"paints":[25],"each":[26],"new":[27],"edge":[28],"red":[29],"or":[30],"blue":[31],"after":[32],"it":[33],"is":[34,39,46,65,80,100,113],"built.":[35],"graph":[37,51,79,98],"constructed":[38],"background":[42,50,78],"graph.":[43,116],"Builder's":[44],"goal":[45,60,64,115],"to":[47,52,66,82],"cause":[48],"contain":[53],"monochromatic":[55],"copy":[56],"of":[57,73,96,133],"given":[59],"graph,":[61],"Painter's":[63],"prevent":[67],"this.":[68],"In":[69],"$S_k$-game":[71,109],"variant":[72],"typical":[75],"game,":[76],"constrained":[81],"have":[83],"maximum":[84],"degree":[85,92],"no":[86],"greater":[87],"than":[88],"$k$.":[89],"on-line":[91],"number":[94],"$\\mathring{R}_{\\Delta}(G)$":[95],"$G$":[99,112,124],"minimum":[102],"$k$":[103],"such":[104],"that":[105],"wins":[107],"an":[108],"in":[110],"which":[111],"Butterfield":[117],"et":[118],"al.":[119],"previously":[120],"determined":[121],"all":[122],"graphs":[123],"satisfying":[125,136],"$\\mathring{R}_{\\Delta}(G)\\le":[126],"3$.":[127],"We":[128],"provide":[129],"complete":[131],"classification":[132],"trees":[134],"$T$":[135],"$\\mathring{R}_{\\Delta}(T)=4$.":[137]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}