K 4-free subgraphs of random graphs revisited

Abstract

In Combinatorica 17(2), 1997, Kohayakawa, Łuczak and Rödl state a conjecture which has several implications for random graphs. If the conjecture is true, then, for example, an application of a version of Szemerédi’s regularity lemma for sparse graphs yields an estimation of the maximal number of edges in an H-free subgraph of a random graph G n, p . In fact, the conjecture may be seen as a probabilistic embedding lemma for partitions guaranteed by a version of Szemerédi’s regularity lemma for sparse graphs. In this paper we verify the conjecture for H = K 4, thereby providing a conceptually simple proof for the main result in the paper cited above.

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Correspondence to S. Gerke.

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Supported by DFG-Grant Ste 464/3-1.

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Gerke, S., Prömel, H.J., Schickinger, T. et al. K 4-free subgraphs of random graphs revisited. Combinatorica 27, 329–365 (2007). https://doi.org/10.1007/s00493-007-2010-5

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Mathematics Subject Classification (2000)

  • 05C80
  • 05C35