Degree conditions and fractional $k$-factors of graphs
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 353-363
https://doi.org/10.4134/BKMS.2011.48.2.353
Printed March 1, 2011
Sizhong Zhou
Jiangsu University of Science and Technology
Abstract : 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
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