关于指数为(h+1)的临界 h 棱连通图的最大棱数

On the Maximum Size of Critically h-Edge-Connected Graphs with lndex Number h+1

令N 是正整数集合.设p,h∈N,令(?)_h^1(p)是其指数不为1的p 阶临界h 棱连通图集合,f_h^(?)(p)是一个确定的二元函数.本文证明如下结论:设h,p_0∈N,p≥4h-2,h≥4且设G 是(?)_h^1(p_0)中具有最大棱数且指数为h+1的图.如果对任何p∈N 且p<p_0,(?)_h^1(p)中任何图H 的棱数都小于f_H^(?)(p),那么G 的棱数小于f_H~*(p_0).

Let p,h be integers and (?)_h^1(p)the set of critically h-edge-connected graphs of order p and index number≥h+1,In this paper,the following result is given:Let h,p_0 be integers with p<p_0,p_0≥4h-2,h≥4,and G a graph with maximum size in (?)_n^1(p_0).If the index number of G is h+1 and the size of H is not more than f_h~*(p)-1 for any H∈(?)_h^1(p),the size of G is not more than f_h^1(p_(?))-1,where