【摘要】 既是(g,f)-覆盖又是(g,f)-消去的图称为(g,f)-对等图.给出了有1-因子F的图是(g,f)-对等图、f-对等图的关于F的分支的若干充分条件,证明了如下定理:设G是一个图,F为G的1-因子,w(F)≥2且w(F)≡0(mod 2);g和f是定义在V(G)上的整数值函数并且对每个x∈V(G)都有g(x)≤f(x).若对F的每个分支C=xy,G-{x,y}是(g,f)-对等图,则G也是(g,f)-对等图.并指出定理中的条件在一定意义上是最好可能的.更多还原

【Abstract】 If a graph is(g,f)-covered and(g,f)-deleted,then it is called a(g,f)-uniform graph.Several sufficient conditions about components of factor F for graphs with 1-factors to be(g,f)-uniform,f-uniform are given and the following result is proved: Let G be a graph with 1-factor F such that ω(F)≥2 and ω(F)≡0(mod 2).Let g and f be two integer-valued functions defined on V(G) such that g(x)≤f(x) for each vertex x of V(G).Assume G-{x,y}be(g,f)-uniform for every component C=xy of F,then G is(g,f)-uniform.Furthermore,it has been shown that the conditions in the theorem are best possible in some sense.更多还原