Bulletin of the
Korean Mathematical Society BKMS

Let $k\geq1$ be an integer, and let $G$ be a 2-connected graph of order $n$ with $n\geq\max\{7,4k+1\}$, and the minimum degree $\delta(G)\geq k+1$. In this paper, it is proved that $G$ has a fractional $k$-factor excluding any given edge if $G$ satisfies $\max\{d_G(x),d_G(y)\}\geq\frac{n}{2}$ for each pair of nonadjacent vertices $x,y$ of $G$. Furthermore, it is showed that the result in this paper is best possible in some sense.

Keywords: graph, degree, $k$-factor, fractional $k$-factor

MSC numbers: 05C70