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NEIGHBOURHOOD AND THE EXISTENCE OF FRACTIONAL k-FACTORS OF GRAPHS
Published online by Cambridge University Press: 13 January 2010
Abstract
Let G be a graph, and k a positive integer. Let h:E(G)→[0,1] be a function. If ∑ e∋xh(e)=k holds for each x∈V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh={e∈E(G)∣h(e)>0}. In this paper we use neighbourhoods to obtain a new sufficient condition for a graph to have a fractional k-factor. Furthermore, this result is shown to be best possible in some sense.
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2010
Footnotes
This research was sponsored by Qing Lan Project of Jiangsu Province and was supported by Jiangsu Provincial Educational Department (07KJD110048) and Sichuan Provincial Educational Department (08zb068).
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