{"id":"https://openalex.org/W7201854947","doi":"https://doi.org/10.48550/arxiv.2608.06029","title":"Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs","display_name":"Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs","publication_year":2026,"publication_date":"2026-08-06","ids":{"openalex":"https://openalex.org/W7201854947","doi":"https://doi.org/10.48550/arxiv.2608.06029"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.06029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06029","pdf_url":"https://arxiv.org/pdf/2608.06029","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":"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/2608.06029","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112872864","display_name":"Qing Xia","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xia, Qing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112872864"],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.00139999995008111,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ollivier-ricci-curvature","display_name":"Ollivier-Ricci curvature","score":0.972000002861023},{"id":"https://openalex.org/keywords/hypergraphs","display_name":"hypergraphs","score":0.9319999814033508},{"id":"https://openalex.org/keywords/edge-connectivity","display_name":"edge connectivity","score":0.9869999885559082},{"id":"https://openalex.org/keywords/linear-hypergraphs","display_name":"linear hypergraphs","score":0.6990000009536743},{"id":"https://openalex.org/keywords/k-uniform-hypergraphs","display_name":"k-uniform hypergraphs","score":0.890999972820282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8675000071525574},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6815000176429749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6291999816894531},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5566999912261963},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.4934999942779541},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45809999108314514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45190000534057617},{"id":"https://openalex.org/C2994516854","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Finite graph","level":3,"score":0.44620001316070557},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.42730000615119934},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4185999929904938},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.29600000381469727},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C16063025","wikidata":"https://www.wikidata.org/wiki/Q4370338","display_name":"Total curvature","level":5,"score":0.26429998874664307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.06029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06029","pdf_url":"https://arxiv.org/pdf/2608.06029","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.06029","doi":"https://doi.org/10.48550/arxiv.2608.06029","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.06029","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:2608.06029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.06029","pdf_url":"https://arxiv.org/pdf/2608.06029","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":"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/W7201854947.pdf","grobid_xml":"https://content.openalex.org/works/W7201854947.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4414450626","https://openalex.org/W4415345677","https://openalex.org/W7172442100"],"related_works":["https://openalex.org/W7172442100","https://openalex.org/W3185050346","https://openalex.org/W7221187802","https://openalex.org/W2195176792","https://openalex.org/W2606766893","https://openalex.org/W7098923610","https://openalex.org/W2799844489","https://openalex.org/W6979299635","https://openalex.org/W4414450626","https://openalex.org/W4415345677"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,11,144],"local":[3],"geometric":[4],"criterion":[5],"ensuring":[6],"that":[7,56],"the":[8,35,46,75,95,116,123,136,140,149],"edge-connectivity":[9,82,141],"of":[10,38],"hypergraph":[12,24],"equals":[13],"its":[14],"minimum":[15,78],"incidence":[16,79],"degree:":[17],"every":[18,100],"locally":[19,88],"finite":[20,89],"connected":[21],"$r$-uniform":[22],"linear":[23],"with":[25,45,106],"$r\\ge3$":[26],"and":[27,59,81,112,143],"nonnegative":[28],"Lin--Lu--Yau":[29],"curvature":[30,40],"has":[31],"this":[32],"property.":[33],"Among":[34],"various":[36],"extensions":[37],"Ollivier--Ricci":[39],"to":[41],"hypergraphs,":[42,91],"we":[43,54,92],"work":[44],"equal-edges":[47],"random":[48],"walk":[49],"on":[50,97,115],"hypergraphs":[51,72],"\\cite{CoupetteEtAl2023}.":[52],"Moreover,":[53],"show":[55],"both":[57],"uniformity":[58],"linearity":[60],"are":[61],"essential:":[62],"if":[63],"either":[64],"assumption":[65],"is":[66,83,103,113],"removed,":[67],"there":[68],"exist":[69],"positively":[70],"curved":[71],"for":[73,126],"which":[74],"gap":[76],"between":[77],"degree":[80],"arbitrarily":[84],"large.":[85],"For":[86],"arbitrary":[87],"simple":[90],"also":[93,130],"determine":[94],"dependence":[96],"idleness":[98,101],"completely:":[99],"function":[102],"piecewise":[104],"affine":[105,110,114],"at":[107],"most":[108],"three":[109],"pieces":[111],"universal":[117],"interval":[118],"$[1/2,1]$.":[119],"These":[120],"results":[121],"extend":[122],"corresponding":[124],"theory":[125],"graphs":[127],"\\cite{BourneEtAl2018}.":[128],"They":[129],"provide":[131],"two":[132],"useful":[133],"tools":[134],"below:":[135],"$2$-section":[137],"reduction":[138],"underlying":[139],"argument":[142],"limit-free":[145],"formula":[146],"used":[147],"in":[148],"sharpness":[150],"constructions.":[151]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-08T00:00:00"}
