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A MINIMUM DEGREE CONDITION FOR FRACTIONAL ID-[a,b]-FACTOR-CRITICAL GRAPHS

  • SIZHONG ZHOU (a1), ZHIREN SUN (a2) and HONGXIA LIU (a3)

Abstract

Let G be a graph of order n, and let a and b be two integers with 1≤ab. Let h:E(G)→[0,1] be a function. If a≤∑ exh(e)≤b holds for any xV (G), then we call G[Fh] a fractional [a,b] -factor of G with indicator function h, where Fh ={eE(G):h(e)>0}. A graph G is fractional independent-set-deletable [a,b] -factor-critical (in short, fractional ID-[a,b] -factor-critical) if GI has a fractional [a,b] -factor for every independent set I of G. In this paper, it is proved that if n≥((a+2b)(a+b−2)+1 )/b and δ(G)≥((a+b)n )/(a+2b ) , then G is fractional ID-[a,b] -factor-critical. This result is best possible in some sense, and it is an extension of Chang, Liu and Zhu’s previous result.

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Copyright

Corresponding author

For correspondence; e-mail: zsz_cumt@163.com

Footnotes

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This research was supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (10KJB110003), Jiangsu University of Science and Technology (2010SL101J) and Shandong Province Higher Educational Science and Technology Program (J10LA14), and was sponsored by the Qing Lan Project of Jiangsu Province.

Footnotes

References

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[1]Bondy, J. A. and Murty, U. S. R., Graph Theory with Applications (The Macmillan Press, London, 1976).
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