A Ramsey-style extension of a theorem of Erdős and Hajnal
Volume 170 / 2001
Fundamenta Mathematicae 170 (2001), 119-122
MSC: Primary 05C55, 03E05.
DOI: 10.4064/fm170-1-7
Abstract
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.
