有约束条件的正则图的k—覆盖性质

Regular graphs with prescribed properties and k—covered properties

设n和r为偶数 ,k为奇数 ,n >r>k >0 ,λ≥ 2为整数。G是有n个顶点、边连通度为λ的r—正则图。若λ和n满足下列条件 :( 1)当r≥ 2k时 ,r -λk >0且n <1+( 1+r)k ;( 2 )当r <2k时 ,r+λk -λr>0且n <1+( 1+r) (r-k) 。

Let n>r>k> 0 with n and r even and k odd, and let λ ≥2 be an integer. Let G be an r —regular graph of even order n with edge connectivity λ . If λ and n meet the requirements as follow:(1) r≥2k,r-λk >0 and n<1+(1+r)k ; (2) r<2k,r+λk-λr >0 and n<1+ (1+r)(r-k) , then G is k —covered