The asymptotic of off-diagonal online Ramsey numbers for paths
We prove that for every k≥10, the online Ramsey number for paths Pk and Pn satisfies r̃(Pk,Pn)≥53n+k9−4, matching up to a linear term in k the upper bound recently obtained by Bednarska-Bzdęga (2024). In particular, this implies limn→∞r̃(Pk,Pn)n=53, whenever 10≤k=o(n), disproving a conjecture by Cyman et al. (2015).
Authors
- Julien Portier (ORCID: https://orcid.org/0000-0002-9847-0603)
- Adva Mond (ORCID: https://orcid.org/0000-0002-4805-7503)
Institutions
- University of Cambridge (GB)
Publication Details
- Journal
- European Journal of Combinatorics
- Published
- 2024-08-09
- DOI
- https://doi.org/10.1016/j.ejc.2024.104032
- Citations
- 1
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 1.32