图的1-因子、f-因子和(g,f)-因子

ONE-FACTORS, f-FACTORS AND (g, f)-FACTORS OF GRAPHS

设G是一个图且有一个1-因子F，g和f是定义在V（G）上的非负整数值函数且对每个X∈V(G)有g（X）＜f(X)≤dG（x），且f(v(G))为偶数．（i）若对每个xy∈F有f(x)=f(y)且G－{x,y}有一个（g，f)-因子，则G有一个（g，f)-因子；（ii）若对每个xy∈F有f(X）=f（y）且G-{X，y}有f-因子，则G有f-因子.

Let G be a graph with 1-factor F and let g and f be two non-negative integer-val-ued functions defined on V(G) such that g(x) < f(x) ≤ dG(x) for every x e V(G). Sup-pose f(V(G)) is even. (1) If f(x) = f(y) and G - {x,y} has a (g,f) -factor for every xy F, then G itself has a (g,f) -factor. (2) If f(x) = f(y) and G - {x,y} has a f-factorfor every xye F, then G itself has a f -factor.