{"id":"https://openalex.org/W7223158757","doi":"https://doi.org/10.48550/arxiv.2610.28395","title":"Sprinkling for random regular graphs and Kim-Vu's sandwich conjecture","display_name":"Sprinkling for random regular graphs and Kim-Vu's sandwich conjecture","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223158757","doi":"https://doi.org/10.48550/arxiv.2610.28395"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28395","pdf_url":"https://arxiv.org/pdf/2610.28395","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/2610.28395","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023726998","display_name":"Julien Portier","orcid":"https://orcid.org/0000-0002-5360-6917","observed_orcids":["https://orcid.org/0000-0002-5360-6917","https://orcid.org/0000-0002-9847-0603"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Portier, Julien","raw_affiliation_strings":["Institute of Mathematics , EPFL , Lausanne , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , EPFL , Lausanne , Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023726998"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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":0.00019999999494757503,"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/T11166","display_name":"Analytic Number Theory Research","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/random-regular-graphs","display_name":"random regular graphs","score":0.9359999895095825},{"id":"https://openalex.org/keywords/water-sprinkling","display_name":"sprinkling","score":0.9440000057220459},{"id":"https://openalex.org/keywords/perfect-matchings","display_name":"perfect matchings","score":0.8619999885559082},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.9750000238418579},{"id":"https://openalex.org/keywords/sparse-random-graphs","display_name":"sparse random graphs","score":0.7910000085830688},{"id":"https://openalex.org/keywords/random-graph-models","display_name":"random graph models","score":0.34700000286102295}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.9010999798774719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252999782562256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.774399995803833},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5583000183105469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5149000287055969},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4620000123977661},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27790001034736633}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28395","pdf_url":"https://arxiv.org/pdf/2610.28395","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.2610.28395","doi":"https://doi.org/10.48550/arxiv.2610.28395","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28395","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28395","pdf_url":"https://arxiv.org/pdf/2610.28395","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/W7223158757.pdf","grobid_xml":"https://content.openalex.org/works/W7223158757.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W3103925657","https://openalex.org/W4416621818","https://openalex.org/W7101407365","https://openalex.org/W7125922633"],"related_works":["https://openalex.org/W4290075478","https://openalex.org/W7101407365","https://openalex.org/W3001133135","https://openalex.org/W4406965635","https://openalex.org/W4416621818","https://openalex.org/W3103925657","https://openalex.org/W3159413361","https://openalex.org/W4416606098","https://openalex.org/W2082971831","https://openalex.org/W7097326411"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,30,67,93],"the":[3,20,103,111],"uniform":[4],"random":[5,25,68],"$d$-regular":[6,69],"graph":[7],"model":[8],"on":[9,71],"$n$":[10,31,72],"vertices":[11,73],"is,":[12],"in":[13,92,110],"total":[14],"variation":[15],"distance,":[16],"asymptotically":[17],"close":[18],"to":[19],"union":[21],"of":[22,54,61,80,102,106],"$d$":[23],"uniformly":[24],"edge-disjoint":[26],"perfect":[27],"matchings,":[28],"provided":[29],"is":[32],"even":[33],"and":[34,49,90],"$\u03c9(1)":[35],"=":[36],"d":[37],"\\leq":[38],"n^{1/10}$.":[39],"This":[40,56],"confirms":[41],"a":[42,59,84,98],"conjecture":[43,85,109],"by":[44,86],"Hollom,":[45],"Lichev,":[46],"Mond,":[47],"Portier,":[48],"Wang":[50],"for":[51,77],"this":[52,65],"range":[53,79],"parameters.":[55],"result":[57],"has":[58],"couple":[60],"interesting":[62],"consequences.":[63],"First,":[64],"shows":[66],"graphs":[70],"exhibit":[74],"sprinkling":[75],"properties":[76],"some":[78],"parameters,":[81],"thereby":[82],"confirming":[83],"Isaev,":[87],"McKay,":[88],"Southwell":[89],"Zhukovskii":[91],"range.":[94],"Second,":[95],"we":[96],"give":[97],"short":[99],"alternative":[100],"proof":[101],"upper":[104],"side":[105],"Kim-Vu's":[107],"sandwich":[108],"sparse":[112],"regime.":[113]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}