A Result on Fractional ID-\(k\)-Factor-Critical Graphs

Let \( G \) be a simple graph of order \( n \), and let \( k \) be 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, we obtain a sufficient condition for a graph \( G \) to be fractional ID-\( k \)-factor-critical. Furthermore, it is shown that the result in this paper is best possible in some sense.