Some conditions for hamiltonian cycles in 1-tough $(K_2\cup k{K}_1)$-free graphs

Katsuhiro Ota, Masahiro Sanka

Let $k\ge 2$ be an integer. We say that a graph $G$ is $(K_2\cup k{K}_1)$-free if it does not contain $K_2\cup k{K}_1$ as an induced subgraph. Recently, Shi and Shan conjectured th…