高度不正则树的存在性

EXISTENCE FOR HIGHLY IRREGULAR TREES

本文证明了对不等于3,5,6,7,11,12.13的任意正整数 n,存在 n 阶高度不正则树,同时给出它的最大度d 的上界 d_(max)=[log_z n]和下界 d^(min)=0(n=1).或1(n=2),或2(n=4).或3(n=2~3+6r+s,r=0,1,2,3,….s=0,1,2),或4(n>16且 n≠2~3+6r+s),并证明对任意正整数 k∈[d_(min),d_(max)],存在最大度为 k 的 n 阶高度不正则树.

The paper shows thet there exists a highly irregular tree of order n for each possitive integer n(?) 3,5,6,7,11,12,13,and gives the upper bound d_(max) and the lower bound d_(min) of maximum degree d for a highly irregu- lar tree of order n respectively,d_(max)=[log_2n],d_(min)=0(n=1),or l(n=2),or 2(n=4),or 3(n=2~3+6r+s,r=0,1, 2,3,…,s=0,1,2),or 4(n>16,n(?)2~3+6r+s),and shows that there exists a highly irregular tree of order n with maximum degree k for each integer k(?)[d_(min),d_(max)].