A Sufficient Condition for(g,f)-3-Deleted Graphs

Let G be a graph with vertex set V(G) and edge setE(G),and let g and f be two integer-valued functions defined on V(G) such that gf for every x∈V(G),A(g,f)-factor of G is a spanning subgraph F of G such that g(x)≤dF(x) for every x∈V(G).A graph G is called a(g,f)-3-deleted graph if for any three deges e1,e2,e3,of G,G has a(g,f)-factor excluding w1,e2,e3.In this paper,a sufficient condition for graphs to be(g,f)-3-deleted are given.