路长至少为4的一个Menger型定理

A Mengerian Theorem for paths of Length at Least Four

设G是简单图,HV(G),x,y∈V(G)\H。若G中任何一条长度不小于n的x-y路至少与H有一个交点。则记为(x,H,y)_G^4。本文证明了:若(x,H,y)_G ~4蕴涵|H|≥h,则G中至少存在{h/6}条长度不小于4且相互独立的x-y路。从而对n-4。改进了L.Montcjano和V.Ncumann—Lara的结果。

Let G be a simple graph. HV(G). x, y∈V(G)-H. If every xy -path in G of length greater than or equal to n has at least a vertex in H. then we write (x, H. y)_G^n. In this article we show that if (x, H, y)_G^4 implies |H| ≥h, then there exist at least {h/6} independent xy -paths in G of length grcater than or equal to 4. Hence L. Montcjano and V. Neumann -Lara's result is improved for n=4.