Independence Number and Connectivity for Fractional ID-\(k\)-Factor-Critical Graphs

Let \( G \) be a graph, and \( k \) a positive integer. A graph \( G \) is fractional independent-set-deletable \( k \)-factor-critical (in short, fractional ID-\(k\)-factor-critical) if \( G – I \) has a fractional \( k \)-factor for every independent set \( I \) of \( G \). In this paper, it is proved that if \( \kappa(G) \geq \max \left\{ \frac{k^2 + 6k + 1}{2}, \frac{(k^2 + 6k + 1) \alpha(G)}{4k} \right\} \), then \( G \) is fractional ID-\(k\)-factor-critical.