DC Field | Value | Language |
---|---|---|
dc.contributor.author | Haslegrave, John | ko |
dc.contributor.author | Hyde, Joseph | ko |
dc.contributor.author | Kim, Jaehoon | ko |
dc.contributor.author | Liu, Hong | ko |
dc.date.accessioned | 2023-03-27T05:01:13Z | - |
dc.date.available | 2023-03-27T05:01:13Z | - |
dc.date.created | 2023-03-27 | - |
dc.date.issued | 2023-02 | - |
dc.identifier.citation | FORUM OF MATHEMATICS SIGMA, v.11 | - |
dc.identifier.issn | 2050-5094 | - |
dc.identifier.uri | http://hdl.handle.net/10203/305813 | - |
dc.description.abstract | The Ramsey number R(F, H) is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that, for any graph H, provided n is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: R(C-n, H) = (n - 1)( x(H) - 1) + sigma (H), where sigma(H) is the minimum possible size of a colour class in a x(H)-colouring of H. Allen, Brightwell and Skokan conjectured that the same should be true already when n >= |H|x(H).We improve this 40-year-old result of Burr by giving quantitative bounds of the form n >= C|H| log(4 )x (H), which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs H with large chromatic number. | - |
dc.language | English | - |
dc.publisher | CAMBRIDGE UNIV PRESS | - |
dc.title | Ramsey numbers of cycles versus general graphs | - |
dc.type | Article | - |
dc.identifier.wosid | 000944245500001 | - |
dc.identifier.scopusid | 2-s2.0-85148753000 | - |
dc.type.rims | ART | - |
dc.citation.volume | 11 | - |
dc.citation.publicationname | FORUM OF MATHEMATICS SIGMA | - |
dc.identifier.doi | 10.1017/fms.2023.6 | - |
dc.contributor.localauthor | Kim, Jaehoon | - |
dc.contributor.nonIdAuthor | Haslegrave, John | - |
dc.contributor.nonIdAuthor | Hyde, Joseph | - |
dc.contributor.nonIdAuthor | Liu, Hong | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | 05C55 | - |
dc.subject.keywordAuthor | 05C38 | - |
dc.subject.keywordAuthor | 05C48 | - |
dc.subject.keywordPlus | GOODNESS | - |
dc.subject.keywordPlus | CONJECTURE | - |
dc.subject.keywordPlus | CLIQUE | - |
dc.subject.keywordPlus | PROOF | - |
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