Abstract
ABSTRACTFor , the Erdős–Rogers function measures how large a ‐free induced subgraph there must be in a ‐free graph on vertices. There has been an extensive amount of work towards estimating this function, but until very recently only the case was well understood. A recent breakthrough of Mattheus and Verstraëte on the Ramsey number states that , which matches the known lower bound up to the term. In this paper we build on their approach and generalize this result by proving that holds for every . This comes close to the best known lower bound, improves a substantial body of work, and is the best that any construction of a similar kind can give.
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