A Result on Fractional $ID-k$-Factor-Critical Graphs

Abstract

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.