Every 3-connected claw-free graph with domination number at most 3 is Hamiltonian-connected (Q2142647)

The following conjecture was posed by \textit{W. Zheng} et al. [Discrete Math. 343, No. 1, Article ID 111644, 9 p. (2020; Zbl 1429.05116)]: Every 3-connected claw-free graph with domination number at most 2 is Hamiltonian-connected. In this paper, the authors prove the following stronger theorem which is sharp: Every 3-connected claw-free graph with domination number at most 3 is Hamiltonian-connected. Note that the graphs may admit multiple edges.