Hamiltonian cycles and Hamiltonian paths in $2k$-connected, $1$-tough and $(P_3\cup k{P}_1)$-free graphs

Hui Liu, Yingzhi Tian

A graph $G$ is called Hamiltonian if it possesses a Hamiltonian cycle; and $G$ is called Hamiltonian-connected if it contains a Hamiltonian path between any two distinct vertices.…