Forbidding induced even cycles in a graph: Typical structure and counting

@article{Kim2018ForbiddingIE,
  title={Forbidding induced even cycles in a graph: Typical structure and counting},
  author={Jaehoon Kim and Daniela K{\"u}hn and Deryk Osthus and Timothy Townsend},
  journal={J. Comb. Theory, Ser. B},
  year={2018},
  volume={131},
  pages={170-219}
}
We determine, for all k ≥ 6, the typical structure of graphs that do not contain an induced 2k-cycle. This verifies a conjecture of Balogh and Butterfield. Surprisingly, the typical structure of such graphs is richer than that encountered in related results. The approach we take also yields an approximate result on the typical structure of graphs without an… CONTINUE READING