A NEIGHBORHOOD CONDITION FOR FRACTIONAL ID-[A, B]-FACTOR-CRITICAL GRAPHS

作者：Zhou, Sizhong^*; Yang, Fan^*; Sun, Zhiren^*

来源：Discussiones Mathematicae - Graph Theory, 2016, 36(2): 409-418.

DOI：10.7151/dmgt.1864

• graph
• minimum degree
• neighborhood
• fractional [a, b]-factor
• fractional ID-[a, b]-factor-critical graph

Let C be a graph of order n, and let a and b be two with 1 <= a <= b. Let h : E(G) -> [0, 1] be a function. If a <= Sigma(e) (x) h(e) <= b holds for x is an element of V(G), then we call G[F-h] a fractional [a, b]-factor of G with indicator function h, where F-h = {e is an element of E(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 G - I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if n >= (a+2b) (2a+2b-3) + 1/b , delta(G) >= bn/a+2b + a and vertical bar N-G(x) boolean OR N-G(y)vertical bar >= (a+b)n/a+2b for any two nonadjacent vertices x, y is an element of V(G), then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that this result, is best Possible in some sense.

• 出版日期2016-5
• 单位南京师范大学; 江苏科技大学