More Sufficient Conditions for A Graph to Have ( g , f ) - Factors ∗
نویسندگان
چکیده
Let G be a graph with vertex set V (G) and edge set E(G), and let g and f be integer-valued functions defined on V (G) such that 0 ≤ g(x) < f(x) for all x ∈ V (G), and let H1 and H2 be two edge-disjoint subgraphs of G. We prove that G has a (g, f) -factor F such that E(H1) ⊆ E(F ) and E(H2) ∩ E(F ) = ∅ if G satisfies (1) g(x) + dH2(x) ≤ dG(x) and f(x) ≥ dH1(x) for all x ∈ V (G), and (2) (f(x)− dH1(x))(dG(y)− dH2(y)) ≥ (dG(x)− dH1(x))g(y) for all x, y ∈ V (G).
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