{"id":"https://openalex.org/W1574301979","doi":"https://doi.org/10.37236/2175","title":"Distortion of the Hyperbolicity Constant of a Graph","display_name":"Distortion of the Hyperbolicity Constant of a Graph","publication_year":2012,"publication_date":"2012-03-31","ids":{"openalex":"https://openalex.org/W1574301979","doi":"https://doi.org/10.37236/2175","mag":"1574301979"},"language":"en","primary_location":{"id":"doi:10.37236/2175","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2175","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p67/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/v19i1p67/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031291771","display_name":"Walter Carballosa","orcid":"https://orcid.org/0000-0002-2984-5301"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Walter Carballosa","raw_affiliation_strings":["Charles III University of Madrid"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles III University of Madrid","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024703633","display_name":"Domingo Pestana","orcid":"https://orcid.org/0000-0001-8334-0243"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Domingo Pestana","raw_affiliation_strings":["Charles III University of Madrid"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles III University of Madrid","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002592714","display_name":"Jos\u00e9 M. Rodr\u0131\u0301guez","orcid":"https://orcid.org/0000-0003-2851-7442"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 M. Rodr\u00edguez","raw_affiliation_strings":["Charles III University of Madrid"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles III University of Madrid","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041892602","display_name":"Jos\u00e9 M. Sigarreta","orcid":"https://orcid.org/0000-0002-0863-4695"},"institutions":[{"id":"https://openalex.org/I3130105584","display_name":"Universidad Aut\u00f3noma de Guerrero","ror":"https://ror.org/054tbkd46","country_code":"MX","type":"education","lineage":["https://openalex.org/I3130105584"]},{"id":"https://openalex.org/I4210129481","display_name":"Acapulco Institute of Technology","ror":"https://ror.org/02nrkxp47","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210129481"]},{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES","MX"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 M. Sigarreta","raw_affiliation_strings":["Facultad de Matem\u00e1ticas Universidad Aut\u00f3noma de Guerrero","Col. La Garita, Acapulco, Guerrero, M\u00e9xico","Departamento de Matem\u00e1ticas Universidad Carlos III de Madrid Av. de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas Universidad Aut\u00f3noma de Guerrero","institution_ids":["https://openalex.org/I3130105584"]},{"raw_affiliation_string":"Col. La Garita, Acapulco, Guerrero, M\u00e9xico","institution_ids":["https://openalex.org/I4210129481"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas Universidad Carlos III de Madrid Av. de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3854,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.98150793,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9988999962806702,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9401999711990356,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9312000274658203,"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/geodesic","display_name":"Geodesic","score":0.8639611005783081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8536925315856934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.611229658126831},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6038786768913269},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5023362636566162},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4422883093357086},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4420890808105469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34686166048049927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2893773913383484},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08575162291526794}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8639611005783081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8536925315856934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.611229658126831},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6038786768913269},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5023362636566162},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4422883093357086},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4420890808105469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34686166048049927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2893773913383484},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08575162291526794},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/2175","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2175","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p67/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:10.1.1.225.8417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.225.8417","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/download/v19i1p67/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/2175","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2175","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p67/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":[],"awards":[{"id":"https://openalex.org/G4277135324","display_name":null,"funder_award_id":"MTM2008-02829-E","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5876507022","display_name":null,"funder_award_id":"MTM2009-07800","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1574301979.pdf","grobid_xml":"https://content.openalex.org/works/W1574301979.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1483679902","https://openalex.org/W1514432425","https://openalex.org/W1919435775","https://openalex.org/W1927956358","https://openalex.org/W1971322331","https://openalex.org/W1989128792","https://openalex.org/W1990038669","https://openalex.org/W2010986757","https://openalex.org/W2012993200","https://openalex.org/W2016539414","https://openalex.org/W2028452681","https://openalex.org/W2037909423","https://openalex.org/W2040416454","https://openalex.org/W2044671590","https://openalex.org/W2062886851","https://openalex.org/W2066946920","https://openalex.org/W2070751659","https://openalex.org/W2074778365","https://openalex.org/W2081030240","https://openalex.org/W2089405045","https://openalex.org/W2092489941","https://openalex.org/W2098449770","https://openalex.org/W2113107215","https://openalex.org/W2141063223","https://openalex.org/W2399012647","https://openalex.org/W2625043690","https://openalex.org/W3093149504","https://openalex.org/W4229484577","https://openalex.org/W6600882715"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2998142867","https://openalex.org/W2078299291","https://openalex.org/W1974584795","https://openalex.org/W3111121251","https://openalex.org/W2071383071","https://openalex.org/W2156777494","https://openalex.org/W2008268994","https://openalex.org/W2077696093","https://openalex.org/W3003396734"],"abstract_inverted_index":{"If":[0],"$X$":[1,29],"is":[2,14,30,41,78,85,97,116],"a":[3,10,44,93,103,161],"geodesic":[4,11,56,94],"metric":[5,95],"space":[6,28,96],"and":[7,23],"$x_1,x_2,x_3\\in":[8],"X$,":[9],"triangle":[12,57],"$T=\\{x_1,x_2,x_3\\}$":[13],"the":[15,18,33,47,50,65,90,100,110,122,125,129,135,151,164],"union":[16,48],"of":[17,39,46,49,69,82,92,102,109,113,124,128,155,166,171],"three":[19],"geodesics":[20],"$[x_1x_2]$,":[21],"$[x_2x_3]$":[22],"$[x_3x_1]$":[24],"in":[25,43,59,160,169],"$X$.":[26,60],"The":[27,80],"$\\delta$-hyperbolic":[31],"$($in":[32],"Gromov":[34],"sense$)$":[35],"if":[36],"any":[37,167],"side":[38],"$T$":[40,58],"contained":[42],"$\\delta$-neighborhood":[45],"other":[51,152],"two":[52],"sides,":[53],"for":[54],"every":[55],"We":[61],"denote":[62],"by":[63,138],"$\\delta(X)$":[64],"sharp":[66],"hyperbolicity":[67,91,101,126,165],"constant":[68,127],"$X$,":[70],"i.e.,":[71],"$\\delta(X):=\\inf\\{\\delta\\ge":[72],"0:":[73],"\\,":[74,76],"X":[75],"\\text{":[77],"$\\delta$-hyperbolic}\\,\\}$.":[79],"study":[81],"hyperbolic":[83],"graphs":[84],"an":[86,140],"interesting":[87],"topic":[88],"since":[89],"equivalent":[98],"to":[99,106,117,149],"graph":[104,130,136,168],"related":[105],"it.":[107,145],"One":[108],"main":[111,153],"aims":[112],"this":[114,156],"paper":[115],"obtain":[118,150],"quantitative":[119,162],"information":[120],"about":[121],"distortion":[123],"$G\\setminus":[131],"e$":[132],"obtained":[133],"from":[134,144],"$G$":[137],"deleting":[139],"arbitrary":[141],"edge":[142],"$e$":[143],"These":[146],"inequalities":[147],"allow":[148],"result":[154],"paper,":[157],"which":[158],"characterizes":[159],"way":[163],"terms":[170],"local":[172],"hyperbolicity.":[173]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}