{"id":"https://openalex.org/W7162583412","doi":"https://doi.org/10.4230/lipics.socg.2026.18","title":"Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs","display_name":"Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162583412","doi":"https://doi.org/10.4230/lipics.socg.2026.18"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25824","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.18","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.18/LIPIcs.SoCG.2026.18.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.18/LIPIcs.SoCG.2026.18.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058590949","display_name":"Thomas Bl\u00e4sius","orcid":"https://orcid.org/0000-0003-2450-744X"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bl\u00e4sius, Thomas","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2450-744X","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130258052","display_name":"Emil Dohse","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dohse, Emil","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130274387","display_name":"Deborah Haun","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Haun, Deborah","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0009-0004-2365-0804","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137106864","display_name":"Laura Merker","orcid":"https://orcid.org/0000-0003-1961-4531"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Merker, Laura","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1961-4531","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.88232029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.8219000101089478,"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":0.8219000101089478,"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":0.04839999973773956,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.04479999840259552,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/treewidth","display_name":"Treewidth","score":0.7088000178337097},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5062000155448914},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5022000074386597},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4311000108718872},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.41920000314712524},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.3970000147819519},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.37369999289512634},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.3517000079154968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.833899974822998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8338000178337097},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.7088000178337097},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5066999793052673},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.41920000314712524},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.3970000147819519},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.37369999289512634},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.3517000079154968},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.35030001401901245},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.30489999055862427},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.30059999227523804},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2994000017642975},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.26409998536109924},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25824","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.18","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.18/LIPIcs.SoCG.2026.18.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.socg.2026.18","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.18","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25824","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.18","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.18/LIPIcs.SoCG.2026.18.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162583412.pdf","grobid_xml":"https://content.openalex.org/works/W7162583412.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Hyperbolic":[0],"uniform":[1],"disk":[2,97],"graphs":[3,7,98],"(HUDGs)":[4],"are":[5,80,113,292],"intersection":[6],"of":[8,28,33,63,71,115,119,125,141,145,153,201,208,229,264,290,299],"disks":[9],"with":[10,39,198,211,266],"some":[11,68],"radius":[12,212,267],"r":[13,19,196],"in":[14,30,88,93,99],"the":[15,26,89,100,109,116,151,160,189,199,227,284],"hyperbolic":[16,191],"plane,":[17,102],"where":[18],"may":[20],"be":[21,138,271],"constant":[22,40,53,126,142],"or":[23],"depend":[24],"on":[25],"number":[27,42,200,219,233,289],"vertices":[29],"a":[31,61,85,123,146,154,206,243,251],"family":[32,207],"HUDGs.":[34],"We":[35,174],"show":[36],"that":[37,49,56,78,111,179,215,283],"HUDGs":[38,79,184,210,265,291],"clique":[41,124,218,232],"do":[43],"not":[44,83,157],"admit":[45,185],"product":[46,118,186],"structure,":[47,187],"i.e.,":[48],"there":[50],"is":[51,60,92,106,164,193,234],"no":[52],"c":[54],"such":[55,58],"every":[57,181],"graph":[59,69,140],"subgraph":[62],"H":[64,70,136],"\u22a0":[65],"P":[66],"for":[67,166,180,225],"treewidth":[72,143,230],"at":[73],"most":[74],"c.":[75],"This":[76],"justifies":[77],"described":[81],"as":[82],"having":[84],"grid-like":[86,104,155],"structure":[87,105,156],"literature,":[90],"and":[91,122,223,231,286],"contrast":[94],"to":[95,137,170,242],"unit":[96],"Euclidean":[101],"whose":[103],"evident":[107],"from":[108],"fact":[110],"they":[112],"subgraphs":[114],"strong":[117],"two":[120],"paths":[121],"size":[127],"[Dvo\u0159\u00e1k":[128],"et":[129,256,301],"al.,":[130],"'21,":[131],"MATRIX":[132],"Annals].":[133],"By":[134],"allowing":[135],"any":[139],"instead":[144],"path-like":[147],"graph,":[148],"we":[149],"reject":[150],"possibility":[152],"merely":[158],"by":[159,177,254,273],"maximum":[161],"degree":[162],"(which":[163],"unbounded":[165,221],"HUDGs)":[167],"but":[168,220],"due":[169],"their":[171],"global":[172],"structure.":[173],"complement":[175],"this":[176,248],"showing":[178],"(sub-)constant":[182],"r,":[183],"whereas":[188],"typical":[190],"behavior":[192],"observed":[194],"if":[195],"grows":[197],"vertices.":[202],"Our":[203,279],"proof":[204],"involves":[205],"n-vertex":[209],"log":[213,235,238,239,244,245,268,276],"n":[214,236,246,269,277],"has":[216],"bounded":[217],"treewidth,":[222],"one":[224],"which":[226],"ratio":[228],"/":[237],"n.":[240],"Up":[241],"factor,":[247],"negatively":[249],"answers":[250],"question":[252,298],"raised":[253],"Bl\u00e4sius":[255],"al.":[257,302],"[SoCG":[258],"'25]":[259],"asking":[260],"whether":[261],"balanced":[262],"separators":[263],"can":[270],"covered":[272],"less":[274],"than":[275],"cliques.":[278],"results":[280],"also":[281],"imply":[282],"local":[285],"layered":[287],"tree-independence":[288],"both":[293],"unbounded,":[294],"answering":[295],"an":[296],"open":[297],"Dallard":[300],"[arXiv":[303],"'25].":[304]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-28T00:00:00"}