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Creators/Authors contains: "Luo, Haoran"

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  1. Free, publicly-accessible full text available August 1, 2026
  2. ABSTRACT For graphs and , let be the minimum possible size of a maximum ‐free induced subgraph in an ‐vertex ‐free graph. This notion generalizes the Ramsey function and the Erdős–Rogers function. Establishing a container lemma for the ‐free subgraphs, we give a general upper bound on , assuming the existence of certain locally dense ‐free graphs. In particular, we prove that for every graph with , where , we have For the cases where is a complete multipartite graph, letting , we prove that We also make an observation which improves the bounds of by a polylogarithmic factor. 
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    Free, publicly-accessible full text available January 1, 2026