Abstract: The existence of fractional factors in specific settings is an important topic of graph factor theory, and isolated toughness is an important parameter to measure the vulnerability of networks. As the unique variant of isolation toughness, $I'(G)$ is defined as the minimum ratio of $|S|$ and $i(G-S)-1$, where $S$ is the subset of vertices that satisfies $i(G-S)\ge2$. This parameter measures the robustness of the network from the perspective of topology, and recent research reveals that it is closely related to the fractional factor. In this paper, we give an $I'(G)$ condition for the existence of fractional $[a,b]$-factors in a graph, and show that the condition is sharp by counterexample. This result extends the original $I'(G)$ tight bound on the existence of the fractional $k$-factor.

Key words: graph, fractional factor, fractional$[a,b]$-factor, isolated toughness variant