Dai–Zhang–Broerama–Zhang conjecture on Hamiltonicity of connected K_{1,r}-free split graphs

Let $r$ be an integer with $r\ge 3$. A graph is $K_{1,r}$-free if it has no induced subgraph isomorphic to $K_{1,r}$, and a graph is Hamiltonian if it contains a cycle containing all its vertices. A graph is $k$-connected if deleting fewer than $k$ vertices leaves it connected.

Dai–Zhang–Broerama–Zhang conjecture. Every $(r-1)$-connected $K_{1,r}$-free split graph is Hamiltonian.

The conjecture extends the known cases $r=3$, where it follows from the characterization of Hamiltonian claw-free split graphs, and $r=4$, established by Dai, Zhang, Broerama and Zhang. Its validity for general $r\ge 3$ is not resolved in the supplied source.