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- Title
Multicolor list Ramsey numbers grow exponentially.
- Authors
Fox, Jacob; He, Xiaoyu; Luo, Sammy; Xu, Max Wenqiang
- Abstract
The list Ramsey number Rℓ(H,k) ${R}_{\ell }(H,k)$, recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list‐coloring variant of the classical Ramsey number. They showed that if H $H$ is a fixed r $r$‐uniform hypergraph that is not r $r$‐partite and the number of colors k $k$ goes to infinity, eΩ(k)≤Rℓ(H,k)≤eO(k) ${e}^{{\rm{\Omega }}(\sqrt{k})}\le {R}_{\ell }(H,k)\le {e}^{O(k)}$. We prove that Rℓ(H,k)=eΘ(k) ${R}_{\ell }(H,k)={e}^{{\rm{\Theta }}(k)}$ if and only if H $H$ is not r $r$‐partite.
- Subjects
RAMSEY numbers; RAMSEY theory
- Publication
Journal of Graph Theory, 2022, Vol 101, Issue 3, p389
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22832