{"id":"https://openalex.org/W7221187802","doi":"https://doi.org/10.48550/arxiv.2610.10559","title":"Edge-Connectivity versus Lin--Lu--Yau Curvature","display_name":"Edge-Connectivity versus Lin--Lu--Yau Curvature","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7221187802","doi":"https://doi.org/10.48550/arxiv.2610.10559"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10559","pdf_url":"https://arxiv.org/pdf/2610.10559","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/2610.10559","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043535469","display_name":"Ziming Zhou","orcid":"https://orcid.org/0009-0008-3117-662X","observed_orcids":["https://orcid.org/0009-0008-3117-662X","https://orcid.org/0000-0002-7164-3834"]},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Ziming","raw_affiliation_strings":["School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","Xi'an-Budapest Joint Research Center for Combinatorics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Xi'an-Budapest Joint Research Center for Combinatorics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129607955","display_name":"Shenggui Zhang","orcid":"https://orcid.org/0000-0002-9596-0826","observed_orcids":["https://orcid.org/0000-0002-9596-0826"]},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Shenggui","raw_affiliation_strings":["School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","Xi'an-Budapest Joint Research Center for Combinatorics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Xi'an-Budapest Joint Research Center for Combinatorics , Northwestern Polytechnical University , Xi'an , Shaanxi 710129 , China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9214000105857849,"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":0.9214000105857849,"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/T11476","display_name":"Graph theory and applications","score":0.01769999973475933,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.014600000344216824,"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/edge-connectivity","display_name":"edge connectivity","score":0.9850000143051147},{"id":"https://openalex.org/keywords/graph-curvature","display_name":"graph curvature","score":0.7239999771118164},{"id":"https://openalex.org/keywords/minimum-degree","display_name":"minimum degree","score":0.7620000243186951},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8140000104904175},{"id":"https://openalex.org/keywords/connected-graphs","display_name":"connected graphs","score":0.675000011920929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6567000150680542},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6322000026702881},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6193000078201294},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.564300000667572},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.49810001254081726},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3659999966621399},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.298799991607666},{"id":"https://openalex.org/C2777655698","wikidata":"https://www.wikidata.org/wiki/Q1209358","display_name":"Versa","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29260000586509705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2782000005245209},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10559","pdf_url":"https://arxiv.org/pdf/2610.10559","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.2610.10559","doi":"https://doi.org/10.48550/arxiv.2610.10559","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10559","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10559","pdf_url":"https://arxiv.org/pdf/2610.10559","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221187802.pdf","grobid_xml":"https://content.openalex.org/works/W7221187802.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2103022581","https://openalex.org/W4396815972","https://openalex.org/W4407245124"],"related_works":["https://openalex.org/W6979299635","https://openalex.org/W4414450626","https://openalex.org/W4407245124","https://openalex.org/W3048035890","https://openalex.org/W4290052327","https://openalex.org/W7221055382","https://openalex.org/W7220704761","https://openalex.org/W7171401919","https://openalex.org/W7212013099","https://openalex.org/W7167236677"],"abstract_inverted_index":{"We":[0,34,60],"systematically":[1],"explore":[2],"the":[3,37,47,57,67,79],"relationship":[4],"between":[5],"edge-connectivity":[6,38,68],"and":[7,28,56,77],"Lin--Lu--Yau":[8,21,54,75],"curvature":[9,22,55],"for":[10],"graphs.":[11],"The":[12],"intuition":[13],"is":[14,43],"that":[15,36,72],"a":[16,40,70],"connected":[17,41],"graph":[18,42,71],"with":[19],"large":[20,26],"should":[23],"also":[24,61],"have":[25],"edge-connectivity,":[27],"vice":[29],"versa":[30],"under":[31],"suitable":[32],"conditions.":[33],"prove":[35],"of":[39,49,69,81],"bounded":[44],"lower":[45,64],"by":[46],"product":[48],"its":[50,53],"minimum":[51],"degree,":[52],"constant":[58],"$\\frac{3}{2}$.":[59],"provide":[62],"two":[63],"bounds":[65],"on":[66],"guarantee":[73],"positive":[74],"curvature,":[76],"discuss":[78],"sharpness":[80],"these":[82],"bounds.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}
