@article{18751b05d62f49168a69e37a9ba8a298,

title = "List Ramsey numbers",

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.",

keywords = "Ramsey theory, chromatic number, list coloring",

author = "Noga Alon and Matija Buci{\'c} and Tom Kalvari and Eden Kuperwasser and Tibor Szab{\'o}",

note = "Funding Information: The research on this project was initiated during a joint research workshop of Tel Aviv University and the Free University of Berlin on Graph and Hypergraph coloring Problems, held in Berlin in August 2018, and supported by a GIF grant number G‐1347‐304.6/2016. We would like to thank the German‐Israeli Foundation (GIF) and both institutions for their support. We are extremely grateful to the anonymous referees for their many useful suggestions and comments. Noga Alon research was supported in part by NSF grant number DMS‐1855464, ISF grant number 281/17, GIF grant number G‐1347‐304.6/2016, BSF grant number 2018267, and the Simons Foundation. Matija Buci{\'c} research was supported in part by SNSF grant number 200021‐175573. Tibor Szab{\'o} research was supported in part by GIF grant number G‐1347‐304.6/2016 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy—The Berlin Mathematics Research Center MATH+ (EXC‐2046/1, Project ID: 390685689).",

year = "2020",

doi = "10.1002/jgt.22610",

language = "English (US)",

journal = "Journal of Graph Theory",

issn = "0364-9024",

publisher = "Wiley-Liss Inc.",

}