A sufficient condition for graphs to be fractional (k, m)-deleted graphs

作者：Zhou, Sizhong^*

来源：Applied Mathematics Letters, 2011, 24(9): 1533-1538.

DOI：10.1016/j.aml.2011.03.041

• Graph
• Binding number
• k-factor
• Fractional k-factor
• Fractional (k. m)-deleted graph

Let G be a graph, and k a positive integer. Let h : E(G) -> [0, 1] be a function. If Sigma(e epsilon x) h(e) = k holds for each x epsilon V(G), then we call G vertical bar F(h vertical bar) a fractional k-factor of G with indicator function h where F(h) = {e epsilon E(G) : h(e) > 0}. A graph G is called a fractional (k, m)deleted graph if there exists a fractional k-factor G vertical bar F(h)vertical bar of G with indicator function It such that h(e) = 0 for any e epsilon E(H), where H is any subgraph of G with m edges. In this paper, we use a binding number to obtain a sufficient condition for a graph to be a fractional (k, m)deleted graph. This result is best possible in some sense, and it is an extension of Zhou's previous results.

• 出版日期2011-9
• 单位江苏科技大学