We determine, for all $k\geq 6$, 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 induced $8$-cycle or without an induced $10$-cycle.
|Journal||Journal of Combinatorial Theory. Series B|
|Early online date||7 Mar 2018|
|Publication status||Published - Jul 2018|
- Induced subgraphs
- Random graphs
- Typical structure