On fractional (f,n)-critical graphs

  • Authors:

  • Sizhong Zhou;Qiqing Shen

  • Affiliations:

  • School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China;School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

Let G be a graph of order p, and let a,b and n be nonnegative integers with b=a=2, and let f be an integer-valued function defined on V(G) such that a=X@?V(G),N"G(X)V(G)}. In this paper, it is proved that G is a fractional (f,n)-critical graph if bind(G)(a+b-1)(p-1)(ap-(a+b)-bn+2) and p=(a+b)(a+b-3)a+bn(a-1). Furthermore, it is showed that the result in this paper is best possible in some sense.