{"id":"https://openalex.org/W7211900258","doi":"https://doi.org/10.48550/arxiv.2609.04713","title":"The size-Ramsey numbers of $k$-uniform relaxed $\\ell$-trees","display_name":"The size-Ramsey numbers of $k$-uniform relaxed $\\ell$-trees","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211900258","doi":"https://doi.org/10.48550/arxiv.2609.04713"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04713","pdf_url":"https://arxiv.org/pdf/2609.04713","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-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","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/2609.04713","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130811861","display_name":"Meng Ji","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ji, Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066109543","display_name":"Yulai Ma","orcid":"https://orcid.org/0000-0002-4324-3497","observed_orcids":["https://orcid.org/0000-0002-4324-3497"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Yulai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"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":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/size-ramsey-numbers","display_name":"size Ramsey numbers","score":0.9679999947547913},{"id":"https://openalex.org/keywords/k-uniform-hypergraphs","display_name":"k-uniform hypergraphs","score":0.9649999737739563},{"id":"https://openalex.org/keywords/extremal-hypergraph-theory","display_name":"extremal hypergraph theory","score":0.7239999771118164},{"id":"https://openalex.org/keywords/hypergraph-ramsey-theory","display_name":"hypergraph Ramsey theory","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.864799976348877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7635999917984009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6273000240325928},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47450000047683716},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.26109999418258667}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04713","pdf_url":"https://arxiv.org/pdf/2609.04713","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-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.04713","doi":"https://doi.org/10.48550/arxiv.2609.04713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04713","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-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04713","pdf_url":"https://arxiv.org/pdf/2609.04713","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-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","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/W7211900258.pdf","grobid_xml":"https://content.openalex.org/works/W7211900258.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4386929722","https://openalex.org/W4394779249","https://openalex.org/W4417183010"],"related_works":["https://openalex.org/W7221813654","https://openalex.org/W2158580611","https://openalex.org/W4407837691","https://openalex.org/W2068593598","https://openalex.org/W3158230343","https://openalex.org/W4394708811","https://openalex.org/W2963430192","https://openalex.org/W2021319109","https://openalex.org/W2273961619","https://openalex.org/W2954479486"],"abstract_inverted_index":{"The":[0],"size-Ramsey":[1],"number":[2,14],"$\\widehat{R}_k(\\mathcal":[3],"G)$":[4],"of":[5,15,27,34,55],"a":[6,18,31],"$k$-uniform":[7,19,73],"hypergraph":[8,20],"$\\mathcal":[9,21,28,35],"G$":[10],"is":[11],"the":[12,56],"minimum":[13],"edges":[16,54],"in":[17,59],"H$":[22,29],"such":[23],"that":[24,71],"every":[25,72],"$2$-edge-coloring":[26],"contains":[30],"monochromatic":[32],"copy":[33],"G$.":[36],"Fox":[37],"asked":[38],"whether,":[39],"for":[40,66],"fixed":[41],"$2\\le":[42],"\\ell0$":[43],"depends":[44],"only":[45],"on":[46,78],"$k$":[47],"and":[48],"$\\ell$.":[49],"Moreover,":[50],"any":[51],"two":[52],"distinct":[53],"construction":[57],"intersect":[58],"at":[60],"most":[61],"$2\\ell-k-1$":[62],"vertices.":[63],"In":[64],"contrast,":[65],"$k\\ge":[67],"2\\ell$,":[68],"we":[69],"prove":[70],"relaxed":[74],"$\\ell$-tree":[75],"$\\bar{\\mathcal":[76],"T}_{n,\\ell}^{(k)}$":[77],"$n$":[79],"vertices":[80],"satisfies":[81],"\\[":[82],"\\widehat{R}_k\\bigl(\\bar{\\mathcal":[83],"T}_{n,\\ell}^{(k)}\\bigr)":[84],"=O_{k,\\ell}(n^{2k}).":[85],"\\]":[86]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-08T00:00:00"}