General fractional -factor numbers of graphs

✍ Scribed by Hongliang Lu; Qinglin Yu

• Book ID: 104001039
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 212 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.11.005

✦ Synopsis

Let G be a graph and f an integer-valued function on V (G). Let h be a function that assigns each edge to a number in [0, 1], such that the f -fractional number of G is the supremum of ∑ e∈E(G) h(e) over all fractional functions h satisfying

for every vertex v. In this work, we provide a new formula for computing the fractional numbers by using Lovász's Structure Theorem. This formula generalizes the formula given in [Y. Liu, G.Z. Liu, The fractional matching numbers of graphs, Networks 40 (2002) 228-231] for the fractional matching numbers.