Liu and Ma's admissible-cycle conjecture

Let an admissible set of $k$ cycles be a set of cycles whose lengths form an arithmetic progression of length $k$ with common difference one or two. A graph has minimum degree at least $k+1$ when every vertex has degree at least $k+1$.

Liu and Ma's conjecture. Every graph with minimum degree at least $k+1$ contains $k$ admissible cycles.

This conjecture implies Erdős' question for $k=2$, asking whether every simple graph with minimum degree at least three contains two cycles whose lengths differ by one or two. It was completely resolved by Gao, Huo, Liu and Ma through a unified approach.