Stability Number and k-Hamiltonian [a, b]-factors

Let a, b and k be three integers with \(b>a\ge 2\) and \(k\ge 0\), and let G be a graph. If \(G-U\) contains a Hamiltonian cycle for any \(U\subseteq V(G)\) with \(|U|=k\), then G is called a k-Hamiltonian graph. An [a, b]-factor F of a graph G is Hamiltonian if F admits a Hamiltonian cycle. If \(G-U\) includes a Hamiltonian [a, b]-factor for every subset \(U\subseteq V(G)\) with \(|U|=k\), then we say that G has a k-Hamiltonian [a, b]-factor. In this paper, we prove that if G is a k-Hamiltonian graph with $$ 1\le \alpha (G)\le \frac{4(b-2)(\delta (G)-a-k+1)}{(a+k+1)^{2}}, $$ then G admits a k-Hamiltonian [a, b]-factor. Furthermore, it is shown that this result is sharp.