{"id":"https://openalex.org/W2080385431","doi":"https://doi.org/10.1137/090776317","title":"Routing Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes","display_name":"Routing Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2080385431","doi":"https://doi.org/10.1137/090776317","mag":"2080385431"},"language":"en","primary_location":{"id":"doi:10.1137/090776317","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776317","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/A5032486424","display_name":"W. Li","orcid":"https://orcid.org/0000-0003-3817-7357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei-Tian Li","raw_affiliation_strings":["li37@mailbox.sc.edu and lu@math.sc.edu and yang36@mailbox.sc.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"li37@mailbox.sc.edu and lu@math.sc.edu and yang36@mailbox.sc.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036596371","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0003-0155-2002"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Linyuan Lu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101484171","display_name":"Yiting Yang","orcid":"https://orcid.org/0000-0002-7331-2772"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yiting Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.1801654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"4","first_page":"1482","last_page":"1494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8816825151443481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.801128089427948},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.7924562692642212},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7642127871513367},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6451568007469177},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.543648898601532},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.49112221598625183},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.47909098863601685},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47699597477912903},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4632813334465027},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42106401920318604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07035741209983826}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8816825151443481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.801128089427948},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.7924562692642212},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7642127871513367},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6451568007469177},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.543648898601532},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.49112221598625183},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.47909098863601685},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47699597477912903},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4632813334465027},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42106401920318604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07035741209983826},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090776317","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776317","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.211.1696","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.1696","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/%7Elu/papers/routingnumber.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332377","display_name":"Goddard Space Flight Center","ror":"https://ror.org/0171mag52"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1578099820","https://openalex.org/W1998756491","https://openalex.org/W2013854554","https://openalex.org/W2066732775","https://openalex.org/W2088744235","https://openalex.org/W2097534604","https://openalex.org/W2107997203"],"related_works":["https://openalex.org/W4286907761","https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W3087772622","https://openalex.org/W2161886274","https://openalex.org/W2072510267","https://openalex.org/W2024158969","https://openalex.org/W1525049041"],"abstract_inverted_index":{"The":[0,66],"routing":[1,39,91],"number":[2],"$rt(G)$":[3],"of":[4,18,30,41],"a":[5],"connected":[6],"graph":[7],"G":[8],"is":[9,93],"the":[10,28,38],"minimum":[11],"integer":[12],"r":[13,24],"so":[14],"that":[15,50],"every":[16],"permutation":[17],"vertices":[19],"can":[20],"be":[21],"routed":[22],"in":[23,96],"steps":[25],"by":[26,74],"swapping":[27],"ends":[29],"disjoint":[31],"edges.":[32],"In":[33],"this":[34,97],"paper,":[35],"we":[36],"study":[37],"numbers":[40],"cycles,":[42],"complete":[43],"bipartite":[44],"graphs,":[45],"and":[46,54,77],"hypercubes.":[47],"We":[48,59],"prove":[49,61],"$rt(C_n)=n-1$":[51],"(for":[52],"$n\\geq3$)":[53],"for":[55,64],"$s\\geq":[56],"t$,":[57],"$rt(K_{s,t})=\\lfloor\\frac{3s}{2t}\\rfloor+O(1)$.":[58],"also":[60,94],"$n+1\\leq":[62],"rt(Q_n)\\leq2n-2$":[63],"$n\\geq3$.":[65],"lower":[67],"bound":[68],"$rt(Q_n)\\geq":[69],"n+1$":[70],"was":[71],"previously":[72],"conjectured":[73],"Alon,":[75],"Chung,":[76],"Graham":[78],"[SIAM":[79],"J.":[80],"Discrete":[81],"Math.,":[82],"7":[83],"(1994),":[84],"pp.":[85],"513\u2013530].":[86],"A":[87],"variation,":[88],"called":[89],"fractional":[90],"number,":[92],"considered":[95],"paper.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}