摘要
Let G<sub>1</sub> and G<sub>2</sub> be finite digraphs,both with vertex set V.Suppose that each vertexv of V has nonnegative integers f（v） and g（v） with f（v）≤g（v）,and each arc e of G<sub>4</sub> hasnonnegative integers a<sub>i</sub>（e） and b<sub>i</sub>（e） with a<sub>i</sub>（e）≤b<sub>i</sub>（e）,i=1,2.In this paper we give anecessary and sufficient condition for the existence of k arborescences in G<sub>4</sub> covering each are（?） of G<sub>i</sub> at least a<sub>i</sub>（e） and at most b<sub>i</sub>（e） times,i=1,2,and satisfying the condition that foreach v in Vf（v）≤r<sub>1</sub>（v）=r<sub>2</sub>（v）≤g（v）where r<sub>4</sub>（v） denote the number of the arborescences in G<sub>?</sub> rooted at v.
Let G_1 and G_2 be finite digraphs,both with vertex set V.Suppose that each vertexv of V has nonnegative integers f(v) and g(v) with f(v)≤g(v),and each arc e of G_4 hasnonnegative integers a_i(e) and b_i(e) with a_i(e)≤b_i(e),i=1,2.In this paper we give anecessary and sufficient condition for the existence of k arborescences in G_4 covering each are(?) of G_i at least a_i(e) and at most b_i(e) times,i=1,2,and satisfying the condition that foreach v in Vf(v)≤r_1(v)=r_2(v)≤g(v)where r_4(v) denote the number of the arborescences in G_(?) rooted at v.
基金
Work Supported by the exchange program between the Academia Sinica and the Max Planck Society
