dc.contributor.author
Kathapurkar, A.
dc.contributor.author
Morris, P.
dc.contributor.author
Perarnau, Guillem
dc.date.accessioned
2026-01-20T09:56:45Z
dc.date.issued
2025-11-11
dc.identifier.uri
http://hdl.handle.net/2072/489135
dc.description.abstract
A meta-conjecture of Coulson, Keevash, Perarnau, and Yepremyan [12] states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow version of that spanning structure in any suitably bounded colouring of the host (hyper-)graph. We solve one of the most pertinent outstanding cases of this conjecture by showing that for any 1≤ j ≤ k-1 , if G is a k -uniform hypergraph above the j -degree threshold for a loose Hamilton cycle, then any globally bounded colouring of G contains a rainbow loose Hamilton cycle.
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dc.description.sponsorship
Research supported by EPSRC Research grant EP/R034389/1.Research supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Walter Benjamin programme-project number 504502205 and by the European Union's Horizon Europe Marie Sklodowska-Curie grant RAND-COMB-DESIGN-project number 101106032.Research supported by the grants RED2022-134947-T, PID2023-147202NB-I00, PCI2024-155080-2 and the Programme Severo Ochoa y Maria de Maeztu por Centros y Unidades de Excelencia en I&D (CEX2020-001084-M), all of them funded by MICIU/AEI/10.13039/501100011033.
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dc.format.extent
30 p.
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dc.publisher
Cambridge University Press
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dc.relation.ispartof
Combinatorics, Probability and Computing
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Spanning structures
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dc.subject.other
Hypergraphs
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dc.subject.other
extremal graph theory
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dc.subject.other
local lemma
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dc.title
A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/acceptedVersion
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dc.embargo.terms
6 mesos
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dc.identifier.doi
10.1017/S0963548325100266
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dc.date.embargoEnd
2026-05-10T01:00:00Z
dc.rights.accessLevel
info:eu-repo/semantics/embargoedAccess
