K 4-free graphs without large induced triangle-free subgraphs


Let f 3,4(n), for a natural number n, be the largest integer m such that every K 4-free graph of order n contains an induced triangle-free subgraph of order m. We prove that for every suffciently large n, f 3,4(n)≤n 1/2(lnn)120. By known results, this bound is tight up to a polylogarithmic factor.

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Correspondence to Guy Wolfovitz.

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Wolfovitz, G. K 4-free graphs without large induced triangle-free subgraphs. Combinatorica 33, 623–631 (2013). https://doi.org/10.1007/s00493-013-2845-x

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Mathematics Subject Classification (2010)

  • 05C35
  • 05D40