The asymptotic of off-diagonal online Ramsey numbers for paths
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916351857131520 |
|---|---|
| author | Mond, Adva Portier, Julien |
| author_facet | Mond, Adva Portier, Julien |
| contents | We prove that for every $k\ge 10$, the online Ramsey number for paths $P_k$ and $P_n$ satisfies $\tilde{r}(P_k,P_n) \geq \frac{5}{3}n + \frac{k}{9} - 4$, matching up to a linear term in $k$ the upper bound recently obtained by Bednarska-Bzd{ę}ga. In particular, this implies $\lim_{n \rightarrow \infty} \frac{\tilde{r}(P_k, P_n)}{n} = \frac{5}{3}$, whenever $10 \le k=o(n)$, disproving a conjecture by Cyman, Dzido, Lapinskas and Lo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The asymptotic of off-diagonal online Ramsey numbers for paths Mond, Adva Portier, Julien Combinatorics We prove that for every $k\ge 10$, the online Ramsey number for paths $P_k$ and $P_n$ satisfies $\tilde{r}(P_k,P_n) \geq \frac{5}{3}n + \frac{k}{9} - 4$, matching up to a linear term in $k$ the upper bound recently obtained by Bednarska-Bzd{ę}ga. In particular, this implies $\lim_{n \rightarrow \infty} \frac{\tilde{r}(P_k, P_n)}{n} = \frac{5}{3}$, whenever $10 \le k=o(n)$, disproving a conjecture by Cyman, Dzido, Lapinskas and Lo. |
| title | The asymptotic of off-diagonal online Ramsey numbers for paths |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.16628 |