On rainbow-free colourings of uniform hypergraphs
We study rainbow-free colourings of k-uniform hypergraphs; that is, colourings that use k colours but with the property that no hyperedge attains all colours. We show that p⁎ = (k−1)(lnn)/n is the threshold function for the existence of a rainbow-free colouring in a random k-uniform hypergraph....
| Egile Nagusiak: | , |
|---|---|
| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
Elsevier
2021
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| _version_ | 1826307854102953984 |
|---|---|
| author | Groot Koerkamp, R Živný, S |
| author_facet | Groot Koerkamp, R Živný, S |
| author_sort | Groot Koerkamp, R |
| collection | OXFORD |
| description | We study rainbow-free colourings of k-uniform hypergraphs; that is, colourings that use k colours but with the property that no hyperedge attains all colours. We show that p⁎ = (k−1)(lnn)/n is the threshold function for the existence of a rainbow-free colouring in a random k-uniform hypergraph. |
| first_indexed | 2024-03-07T07:10:54Z |
| format | Journal article |
| id | oxford-uuid:7acf9e98-2b4a-4e9e-9d7d-35cfdb97e3e6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:10:54Z |
| publishDate | 2021 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:7acf9e98-2b4a-4e9e-9d7d-35cfdb97e3e62022-06-17T09:01:22ZOn rainbow-free colourings of uniform hypergraphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7acf9e98-2b4a-4e9e-9d7d-35cfdb97e3e6EnglishSymplectic ElementsElsevier2021Groot Koerkamp, RŽivný, SWe study rainbow-free colourings of k-uniform hypergraphs; that is, colourings that use k colours but with the property that no hyperedge attains all colours. We show that p⁎ = (k−1)(lnn)/n is the threshold function for the existence of a rainbow-free colouring in a random k-uniform hypergraph. |
| spellingShingle | Groot Koerkamp, R Živný, S On rainbow-free colourings of uniform hypergraphs |
| title | On rainbow-free colourings of uniform hypergraphs |
| title_full | On rainbow-free colourings of uniform hypergraphs |
| title_fullStr | On rainbow-free colourings of uniform hypergraphs |
| title_full_unstemmed | On rainbow-free colourings of uniform hypergraphs |
| title_short | On rainbow-free colourings of uniform hypergraphs |
| title_sort | on rainbow free colourings of uniform hypergraphs |
| work_keys_str_mv | AT grootkoerkampr onrainbowfreecolouringsofuniformhypergraphs AT zivnys onrainbowfreecolouringsofuniformhypergraphs |