{"id":"https://openalex.org/W7140162405","doi":"https://doi.org/10.48550/arxiv.2603.22204","title":"Separators for intersection graphs of spheres","display_name":"Separators for intersection graphs of spheres","publication_year":2026,"publication_date":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140162405","doi":"https://doi.org/10.48550/arxiv.2603.22204"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Fox, Jacob","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fox, Jacob","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Tidor, Jonathan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tidor, Jonathan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.44600000977516174,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.44600000977516174,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.23399999737739563,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.07039999961853027,"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/spheres","display_name":"SPHERES","score":0.7836999893188477},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6588000059127808},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5655999779701233},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.5404000282287598},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.48240000009536743},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4507000148296356}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7836999893188477},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6934000253677368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6909999847412109},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6588000059127808},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5655999779701233},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.5404000282287598},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4507000148296356},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.34130001068115234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32260000705718994},{"id":"https://openalex.org/C103368685","wikidata":"https://www.wikidata.org/wiki/Q638846","display_name":"Intersection number","level":3,"score":0.298799991607666},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.2648000121116638}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,53,61],"existence":[3],"of":[4,10,19,28,42,52],"optimal":[5],"separators":[6],"for":[7],"intersection":[8,26],"graphs":[9],"balls":[11,62],"and":[12,63,71],"spheres":[13,30,64],"in":[14,31,50],"any":[15],"dimension":[16],"$d$.":[17],"One":[18],"our":[20],"results":[21],"is":[22,47],"that":[23],"if":[24,60],"an":[25],"graph":[27],"$n$":[29],"$\\mathbb{R}^d$":[32],"has":[33],"$m$":[34],"edges,":[35],"then":[36],"it":[37],"contains":[38],"a":[39],"balanced":[40],"separator":[41],"size":[43],"$O_d(m^{1/d}n^{1-2/d})$.":[44],"This":[45],"bound":[46],"best":[48],"possible":[49],"terms":[51],"parameters":[54],"involved.":[55],"The":[56],"same":[57],"result":[58],"holds":[59],"are":[65],"replaced":[66],"by":[67],"fat":[68],"convex":[69],"bodies":[70],"their":[72],"boundaries.":[73]},"counts_by_year":[],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2026-03-25T00:00:00"}