{"id":"https://openalex.org/W2027372468","doi":"https://doi.org/10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","title":"Diameter-preserving orientations of the torus","display_name":"Diameter-preserving orientations of the torus","publication_year":1998,"publication_date":"1998-08-01","ids":{"openalex":"https://openalex.org/W2027372468","doi":"https://doi.org/10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","mag":"2027372468"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5110855641","display_name":"Jean\u2010Claude K\u00f6nig","orcid":null},"institutions":[{"id":"https://openalex.org/I88467170","display_name":"Universit\u00e9 d'\u00c9vry Val-d'Essonne","ror":"https://ror.org/00e96v939","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954","https://openalex.org/I88467170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Claude Konig","raw_affiliation_strings":["LaMI, Universite\u0301 d'Evry, 91025 Evry cedex, France","LaMI, Universit\u00e9 d'Evry, 91025 Evry cedex, France"],"affiliations":[{"raw_affiliation_string":"LaMI, Universite\u0301 d'Evry, 91025 Evry cedex, France","institution_ids":["https://openalex.org/I88467170"]},{"raw_affiliation_string":"LaMI, Universit\u00e9 d'Evry, 91025 Evry cedex, France","institution_ids":["https://openalex.org/I88467170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083263074","display_name":"David W. Krumme","orcid":null},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David W. Krumme","raw_affiliation_strings":["Tufts University, Medford, Massachusetts 02155"],"affiliations":[{"raw_affiliation_string":"Tufts University, Medford, Massachusetts 02155","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005448643","display_name":"Emmanuel Lazard","orcid":null},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Lazard","raw_affiliation_strings":["LAMSADE, Universite\u0301 de Paris-Dauphine, 75775 Paris cedex 16, France","LAMSADE, Universit\u00e9 de Paris-Dauphine, 75775 Paris Cedex, 16, France"],"affiliations":[{"raw_affiliation_string":"LAMSADE, Universite\u0301 de Paris-Dauphine, 75775 Paris cedex 16, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I204730241"]},{"raw_affiliation_string":"LAMSADE, Universit\u00e9 de Paris-Dauphine, 75775 Paris Cedex, 16, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083263074"],"corresponding_institution_ids":["https://openalex.org/I121934306"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":2.5422,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88944942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"1","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T12288","display_name":"Optimization and Search Problems","score":0.9986000061035156,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7770200967788696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7463147044181824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6032289862632751},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5879870057106018},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.514782190322876},{"id":"https://openalex.org/keywords/toroid","display_name":"Toroid","score":0.48642492294311523},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.46457159519195557},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.45589613914489746},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2260676622390747},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1923023760318756}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7770200967788696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7463147044181824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6032289862632751},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5879870057106018},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.514782190322876},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.48642492294311523},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.46457159519195557},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.45589613914489746},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2260676622390747},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1923023760318756},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199808)32:1<1::aid-net1>3.0.co;2-g","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.6429","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.6429","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.tufts.edu/~dwk/orient_paper.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2384156839","https://openalex.org/W4321602641","https://openalex.org/W2394251275","https://openalex.org/W2013173893","https://openalex.org/W2163803384","https://openalex.org/W2028500889","https://openalex.org/W3099927136","https://openalex.org/W2321297009","https://openalex.org/W4313654668","https://openalex.org/W2045165793"],"abstract_inverted_index":{"The":[0],"diameter":[1,35],"of":[2,9,12,19,66],"a":[3],"directed":[4,22],"graph":[5,23],"is":[6,24,44],"the":[7,10,13,33,64,70],"maximum":[8],"lengths":[11],"shortest":[14],"paths":[15],"between":[16],"all":[17,48,69],"pairs":[18],"vertices.":[20],"A":[21],"said":[25],"to":[26],"be":[27],"tightly":[28,67],"oriented":[29],"if":[30],"it":[31],"has":[32],"same":[34],"as":[36],"its":[37],"undirected":[38],"image":[39],"graph.":[40],"Our":[41],"main":[42],"result":[43],"tight":[45,78],"orientations":[46],"for":[47,72,85],"sufficiently":[49],"large":[50],"toroids,":[51],"except":[52],"those":[53],"whose":[54],"sizes":[55],"in":[56],"both":[57],"dimensions":[58],"are":[59],"odd.":[60],"We":[61],"also":[62],"prove":[63],"impossibility":[65],"orienting":[68],"toroids":[71],"which":[73],"we":[74,81],"do":[75],"not":[76],"present":[77],"orientations,":[79],"and":[80],"give":[82],"partial":[83],"results":[84],"dimensionality":[86],"higher":[87],"than":[88],"two.":[89],"\u00a9":[90],"1998":[91,100],"John":[92],"Wiley":[93],"&":[94],"Sons,":[95],"Inc.":[96],"Networks":[97],"32:":[98],"1\u201311,":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}