Loading...
Please wait, while we are loading the content...
Similar Documents
Improved Bounds for the Ramsey Number of Tight Cycles Versus Cliques
| Content Provider | Scilit |
|---|---|
| Author | Mubayi, Dhruv |
| Copyright Year | 2016 |
| Description | The 3-uniform tight cycle C_{s}$^{3}$ has vertex set ${\mathbb Z}_s$ and edge set {{i, i + 1, i + 2}: i ∈ ${\mathbb Z}_s$ }. We prove that for every s ≢ 0 (mod 3) with s ⩾ 16 or s ∈ {8, 11, 14} there is a $c_{s}$ > 0 such that the 3-uniform hypergraph Ramsey number r(C_{s}$^{3}$, K_{n}$^{3}$) satisfies $\begin{equation*} r(C_s^3, K_n^3)< 2^{c_s n \log n}.\ \end{equation*}$ This answers in a strong form a question of the author and Rödl, who asked for an upper bound of the form $2^{n^{1+\epsilon_s}}$ for each fixed s ⩾ 4, where $ε_{s}$ → 0 as s → ∞ and n is sufficiently large. The result is nearly tight as the lower bound is known to be exponential in n. |
| Related Links | http://arxiv.org/pdf/1511.09104 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5980C527685C7E3ADBC2D4B7B3D9F2FB/S0963548316000080a.pdf/div-class-title-improved-bounds-for-the-ramsey-number-of-tight-cycles-versus-cliques-div.pdf |
| Ending Page | 796 |
| Page Count | 6 |
| Starting Page | 791 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548316000080 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 5 |
| Volume Number | 25 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2016-09-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Mathematical Physics Primary 05c65 Secondary 05d10 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
