Some remarks about factors of graphs

@article{Correa2008SomeRA,
  title={Some remarks about factors of graphs},
  author={J. R. Correa and M. Matamala},
  journal={J. Graph Theory},
  year={2008},
  volume={57},
  pages={265-274}
}
A (g, f )-factor of a graph is a subset F of E such that for all v ∈ V, g(v) ≤ degF(v) ≤ f(v). Lovasz gave a necessary and sufficient condition for the existence of a (g, f )-factor. We extend, to the case of edge-weighted graphs, a result of Kano and Saito who showed that if g(v) < λdegE(v) < f(v) for any λ ∈ [0, 1], then a (g, f )-factor always exist. In addition, we use results of Anstee to provide new necessary and sufficient conditions for the existence of a (g, f )-factor. © 2008 Wiley… Expand
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