Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n – 1)-odd factor where U is any subset of V(G) such that |U| = k.
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