@article{Shirazi2008ANO,
title={A Note on Polynomials and f-Factors of Graphs},
author={Hamed Shirazi and Jacques Verstra{\"e}te},
journal={Electr. J. Comb.},
year={2008},
volume={15}
}

Let G = (V,E) be a graph, and let f : V → 2 be a function assigning to each v ∈ V a set of integers in {0, 1, 2, . . . , d(v)}, where d(v) denotes the degree of v in G. Lovász [5] defines an f -factor of G to be a spanning subgraph H of G in which dH(v) ∈ f(v) for all v ∈ V . Using the combinatorial nullstellensatz of Alon [2], we prove that if |f(v)| > d 12d(v)e for all v ∈ V , then G has an f -factor. This result is best possible and verifies a conjecture of Addario-Berry, Dalal, Reed and… CONTINUE READING