Cho et al.'s spectral conjecture for [a,b]-factors

Let $G$ be an $n$-vertex graph, and let $b\ge a$ be two positive integers such that $na\equiv 0\pmod{2}$ and $n\ge a+1$. Here, $\lambda(G)$ denotes the spectral radius of $G$, $K_{a-1}\lor(K_1\cup K_{n-a})$ is the join of $K_{a-1}$ with the disjoint union of $K_1$ and $K_{n-a}$, and an $[a,b]$-factor is a spanning subgraph whose vertex degrees lie between $a$ and $b$. Cho et al.'s spectral conjecture. If

$$\lambda(G)>\lambda\bigl(K_{a-1}\lor(K_1\cup K_{n-a})\bigr),$$

then $G$ contains an $[a,b]$-factor. This conjecture proposes a spectral-radius sufficient condition for the existence of an $[a,b]$-factor. Its resolution is not specified in the supplied text.