List Ramsey numbers

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 ℓ‐uniform cliques we prove that the l...

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Bibliographic Details
Published inJournal of graph theory Vol. 96; no. 1; pp. 109 - 128
Main Authors Alon, Noga, Bucić, Matija, Kalvari, Tom, Kuperwasser, Eden, Szabó, Tibor
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.01.2021
Subjects
chromatic number
Exponential functions
list coloring
Ramsey theory
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Summary: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 ℓ‐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.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22610