摘要
In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference Δ between g(x) and f(x) for every vertex x in G. These obtained new degree conditions reformulate Gao’s previous conclusions, and show how Δ acts in the results. Furthermore,counterexamples are structured to reveal the sharpness of degree conditions in the setting f(x) =g(x) + Δ.
In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference Δ between g(x) and f(x) for every vertex x in G. These obtained new degree conditions reformulate Gao’s previous conclusions, and show how Δ acts in the results. Furthermore,counterexamples are structured to reveal the sharpness of degree conditions in the setting f(x) =g(x) + Δ.
基金
Supported by NSFC(Grant Nos.11761083,11771402 and 11671053)
Fundacion Seneca(Spain)(Grant No.20783/PI/18)
Ministry of Science,Innovation and Universities(Spain)(Grant No.PGC2018-097198-B-100)。
