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Let G be a graph and g, f: V (G) 2N be two set functions such that g (v) f (v) and g (v) f (v) 2 for every v V (G). An orientation O of G is called a (g, f) -parity orientation if g (v) d^+O (v) f (v) and g (v) d^+O (v) 2 for every v V (G). In this paper, we give a Tutte-type characterization for a graph to have a (g, f) -parity orientation.
Lu et al. (Sat,) studied this question.
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