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Free, publicly-accessible full text available August 1, 2026
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Balogh, József; Chen, Ce; Luo, Haoran (, Random Structures & Algorithms)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.more » « lessFree, publicly-accessible full text available January 1, 2026
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Balogh, József; Luo, Haoran (, Combinatorica)
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Balogh, József; Chen, Ce; Hendrey, Kevin; Lund, Ben; Luo, Haoran; Tompkins, Casey; Tran, Tuan (, Combinatorica)
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Balogh, József; Krueger, Robert A.; Luo, Haoran (, Random Structures & Algorithms)
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