{"id":"https://openalex.org/W7214948628","doi":"https://doi.org/10.48550/arxiv.2609.36186","title":"Additive Quasi-isometry via rooted graph partitions and layering partition","display_name":"Additive Quasi-isometry via rooted graph partitions and layering partition","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214948628","doi":"https://doi.org/10.48550/arxiv.2609.36186"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36186","pdf_url":"https://arxiv.org/pdf/2609.36186","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36186","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035473225","display_name":"Dibyayan Chakraborty","orcid":"https://orcid.org/0000-0003-0534-6417","observed_orcids":["https://orcid.org/0000-0003-0534-6417","https://orcid.org/0000-0002-1707-0967"]},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chakraborty, Dibyayan","raw_affiliation_strings":["School of Computer Science , University of Leeds , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science , University of Leeds , United Kingdom","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108138645","display_name":"Yann Vax\u00e8s","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vax\u00e8s, Yann","raw_affiliation_strings":["Laboratoire d'Informatique et Syst\u00e8mes , Aix-Marseille Universit\u00e9 and CNRS , Facult\u00e9 des Sciences de Luminy , F-13288 Marseille , Cedex 9 , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique et Syst\u00e8mes , Aix-Marseille Universit\u00e9 and CNRS , Facult\u00e9 des Sciences de Luminy , F-13288 Marseille , Cedex 9 , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210114274"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9672999978065491,"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":0.9672999978065491,"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":0.015699999406933784,"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":0.0031999999191612005,"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/graph-partitioning","display_name":"graph partitioning","score":0.6449999809265137},{"id":"https://openalex.org/keywords/treewidth","display_name":"treewidth","score":0.9259999990463257},{"id":"https://openalex.org/keywords/graph-subdivision","display_name":"graph subdivision","score":0.7770000100135803},{"id":"https://openalex.org/keywords/graph-minors","display_name":"graph minors","score":0.33799999952316284}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7894999980926514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742000222206116},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6463000178337097},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5922999978065491},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5403000116348267},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.510200023651123},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.39719998836517334},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.31209999322891235},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.31040000915527344},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.30809998512268066},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.3050000071525574},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C58228413","wikidata":"https://www.wikidata.org/wiki/Q15704639","display_name":"Induced path","level":5,"score":0.29499998688697815},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.29170000553131104},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C176055353","wikidata":"https://www.wikidata.org/wiki/Q1402114","display_name":"Layering","level":2,"score":0.2703999876976013}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36186","pdf_url":"https://arxiv.org/pdf/2609.36186","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36186","doi":"https://doi.org/10.48550/arxiv.2609.36186","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36186","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36186","pdf_url":"https://arxiv.org/pdf/2609.36186","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214948628.pdf","grobid_xml":"https://content.openalex.org/works/W7214948628.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W4384648187","https://openalex.org/W4406733406","https://openalex.org/W4407126894","https://openalex.org/W4414820644","https://openalex.org/W4415083311","https://openalex.org/W4416050889","https://openalex.org/W7092296238","https://openalex.org/W7123262670","https://openalex.org/W7213371146"],"related_works":["https://openalex.org/W7117532571","https://openalex.org/W4414820644","https://openalex.org/W4415083311","https://openalex.org/W7152507009","https://openalex.org/W7081570766","https://openalex.org/W4384648187","https://openalex.org/W4417513105","https://openalex.org/W7202261071","https://openalex.org/W7092296238","https://openalex.org/W4406733500"],"abstract_inverted_index":{"For":[0,29],"a":[1,74,84],"graph":[2,75,161],"$H$,":[3],"$\\langle":[4,55],"H":[5,56],"\\rangle$":[6,57],"denotes":[7,17],"the":[8,18,27,120,130,135,153,159],"class":[9],"of":[10,13,20,51,92,125,158],"all":[11,156],"subdivisions":[12,157],"$H$":[14],"and":[15,54,62,95,134,155],"$tw(H)$":[16],"treewidth":[19],"$H$.":[21],"In":[22],"this":[23],"paper,":[24],"we":[25,98,128],"prove":[26],"following.":[28],"$k\\geq":[30],"1,":[31],"R\\geq":[32],"1$,":[33],"let":[34],"$G,H$":[35],"be":[36],"two":[37],"graphs":[38,104],"such":[39,80],"that":[40,81,101],"strong":[41,164],"isometric":[42,165],"path":[43,166],"complexities":[44],"(Chakraborty":[45],"et":[46,141],"al.":[47,142],"[\\textsc{Disc.":[48],"Math.,":[49],"2026}])":[50],"both":[52,152],"$G$":[53,63,82],"are":[58],"at":[59],"most":[60],"$k$,":[61],"admits":[64,83],"an":[65,115],"honest,":[66],"``nicely":[67],"rooted''":[68],"$R$-bounded":[69],"$H$-partition.":[70],"Then,":[71],"there":[72],"is":[73],"$F$":[76],"with":[77,107],"$tw(F)\\leq":[78],"tw(H)$":[79],"$(1,33\\cdot":[85],"R\\cdot":[86],"k^2)$-quasi-isometry":[87],"to":[88,110,147],"$F$.":[89],"Using":[90],"results":[91],"Albrechtsen,":[93],"Distel,":[94],"Georgakopoulos":[96],"(2025),":[97],"also":[99],"obtain":[100,148],"$K_{2,t}$-asymptotic":[102],"minor-free":[103],"admit":[105],"quasi-isometries":[106],"additive":[108,149],"distortion":[109],"$K_{2,t}$-minor-free":[111],"graphs.":[112],"This":[113],"answers":[114],"open":[116],"question":[117],"raised":[118],"by":[119],"above":[121],"authors.":[122],"As":[123],"part":[124],"our":[126],"proof,":[127],"combine":[129],"graph-partition":[131],"based":[132,138],"method":[133,139],"layering":[136],"partition":[137],"(Chepoi":[140],"[\\textsc{Discrete":[143],"Comput.":[144],"Geom.}":[145],"2012])":[146],"quasi-isometry":[150],"when":[151],"source":[154],"target":[160],"have":[162],"bounded":[163],"complexity.":[167]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
