Searching Minimum Fractional 1-Factor in Graphs

Spanning subgraph is necessary for the communication in networks. For example, the malfunctioning of one or more nodes in a network in general affects both the global and the local properties of the remaining nodes, because it makes some edges unusable and destroys the connectivity of the system. In this study, we focus on the characters of a network to be fractional-$r$-factors, fractional $(r,k)$-extendable and fractional $(r,n)$-deleteble. An efficient algorithm, based on a result which indicate that $G$ has a minimum fractional 1-factor whose indictor function defined on $\{1, {1\over 2}\}$ if $G$ has a fractional 1-factor, were designed to find a minimum fractional 1-factor.