A sufficient condition for graphs to be fractional -deleted graphs

✍ Scribed by Sizhong Zhou

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 218 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2011.03.041

✦ Synopsis

graph a b s t r a c t Let G be a graph, and k a positive integer. Let h : E(G) → [0, 1] be a function. If ∑ e∋x h(e) = k holds for each x ∈ V (G), then we call G[F h ] a fractional k-factor of G with indicator function h where F h = {e ∈ E(G) : h(e) > 0}. A graph G is called a fractional (k, m)deleted graph if there exists a fractional k-factor G[F h ] of G with indicator function h such that h(e) = 0 for any e ∈ 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.