A remark about fractional (f, n)-critical graphs

作者：Zhou, Sizhong^*; Bian, Qiuxiang; Liu, Hongxia

来源：Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 2011, 19(1): 365-371.

• graph
• binding number
• minimum degree
• fractional f-factor
• fractional (f, n)-critical graph

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 <= f(x) <= b for each x <= V(G). A fractional f-factor is a function h that assigns to each edge of a graph G a number in [0,1], so that for each vertex x we have d(G)(h)(X) = f(x), where d(G)(h)(X) = Sigma(e(sic)x) h(e) (the sum is taken over all edges incident to x) is a fractional degree of x in G. Then a graph G is called a fractional (f,n)-critical graph if after deleting any n vertices of G the remaining graph of G has a f fractional f-factor. The binding number bind(G) is defined as follows,
bind (G) = min{|N(G)(X)|/|X|: empty set not equal X subset of V(G), N(G)(X) not equal V(G)}.
In this paper, it is proved that G is a fractional (f,n)-critical graph if p >= (1+b-1)(1+b-2)-2/a + bn/a-1, bind(G) >= (a+b-1)(p-1)/a(p-1)-bn and delta(G) not equal [(b-1)p+a+b+bn-2/a+b-1].

• 出版日期2011
• 单位烟台大学; 江苏科技大学