\(K_4\)-free graphs without large induced triangle-free subgraphs (Q2250854)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(K_4\)-free graphs without large induced triangle-free subgraphs |
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\(K_4\)-free graphs without large induced triangle-free subgraphs (English)
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21 July 2014
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For natural numbers \(r\), \(s\) and \(n\), let \(f_{r,s}(n)\) be the largest integer \(m\) such that every \(K_s\)-free subgraph of order \(n\) contains an induced \(K_r\)-free subgraph of order \(m\). The author presents an upper bound for \(f_{3,4}(n)\), and determines \(\ln f_{3,4}(n)\) asymptotically.
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triangle-free subgraph
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random graphs
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probabilistic method
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