### Abstract

We introduce a list-coloring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are far apart. For (Formula presented.) -uniform cliques we prove that the list Ramsey number is bounded by an exponential function, while it is well known that the Ramsey number is superexponential for uniformity at least 3. This is in great contrast to the graph case where we cannot even decide the question of equality for cliques.

Original language | English (US) |
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Journal | Journal of Graph Theory |

DOIs | |

State | Accepted/In press - 2020 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Keywords

- chromatic number
- list coloring
- Ramsey theory

## Fingerprint Dive into the research topics of 'List Ramsey numbers'. Together they form a unique fingerprint.

## Cite this

Alon, N., Bucić, M., Kalvari, T., Kuperwasser, E., & Szabó, T. (Accepted/In press). List Ramsey numbers.

*Journal of Graph Theory*. https://doi.org/10.1002/jgt.22610