A Ramsey-style extension of a theorem of Erdős and Hajnal

Volume 170 / 2001

Peter Komjáth Fundamenta Mathematicae 170 (2001), 119-122 MSC: Primary 05C55, 03E05. DOI: 10.4064/fm170-1-7


If $n$, $t$ are natural numbers, $\mu $ is an infinite cardinal, $G$ is an $n$-chromatic graph of cardinality at most $\mu $, then there is a graph $X$ with $X\to (G)^1_\mu $, $|X|=\mu ^+$, such that every subgraph of $X$ of cardinality $< t$ is $n$-colorable.


  • Peter KomjáthDepartment of Computer Science
    Eötvös University
    Kecskeméti u. 10–12
    1053 Budapest, Hungary

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