Some Results on Fractional Covered Graphs∗
نویسندگان
چکیده
Let G = (V (G),E(G)) be a graph. and let g, f be two integer-valued functions defined on V (G) such that g(x)≤ f (x) for all x ∈V (G). G is called fractional (g, f )-covered if each edge e of G belongs to a fractional (g, f )-factor Gh such that h(e) = 1, where h is the indicator function of Gh. In this paper, sufficient conditions related to toughness and isolated toughness for a graph to be fractional 1-covered, 2-covered are given. The results are proved to be best possible in some sense. In particular, a necessary and sufficient condition for a (g, f )-factor covering a given k-matching is obtained.
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