A SUFFICIENT CONDITION FOR A GRAPH TO BE A FRACTIONAL (f, n)-CRITICAL GRAPH

作者：Zhou, Sizhong^*

来源：Glasgow Mathematical Journal, 2010, 52: 409-415.

DOI：10.1017/S001708951000011X

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Let a, b and n be non-negative integers such that 1 <= a <= b, and let G be a graph of order j, with p >= (a+b-1)(a+b-2))+bn-2 and f be an integer-valued function defined on V(G) such that a <= f(x) <= b for all x E V(G). Let h: [0, 1] be a function. If Sigma e is an element of x h(e) = f(x) holds for any x is an element of V(G), then we call G[F(h)] a fractional f-factor of G with indicator function h, where Fh = {e is an element of E(G) : h(e) > 0). A graph G is called a fractional (f, n)-critical graph if after deleting any /7 vertices of G the remaining graph of G has a fractionalf-factor. In this paper, it is proved that G is a fractional (f, n)-critical graph if vertical bar N(G)(X)vertical bar > (b-1)p+vertical bar X vertical bar+bn-1/a+b-1 for every non-empty independent subset X of V(G), and delta(G) > (b-1)p+a+b+bn-2/a+b-1 Furthermore, it is shown that the result in this paper is best possible in some sense.

• 出版日期2010-5
• 单位江苏科技大学