Characterizations of maximum fractional (g,f) ( g , f ) -factors of graphs ?
In this paper a characterization of maximum fractional (g,f) ( g , f ) -factors of a graph is presented. The properties of the maximum fractional (g,f) ( g , f ) -factors and fractional (g,f) ( g , f ) -factors with the minimum of edges are also given, generalizing the results given in[William Y.C. Chen, Maximum (g,f g , f )-factors of a general graph, Discrete Math. 91 (1991) 17] and [Edward R. Scheinerman, Daniel H. Ullman, Fractional Graph Theory, John Wiley and Sonc, Inc., New York, 1997]. Furthermore, some new results on fractional factors are obtained which may be used in the design of networks. A polynomial time algorithm can be obtained for actually finding such maximum fractional (g,f) ( g , f ) -factors in a graph from the proof.
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