Harary图的偶匹配可扩性

Bipartite Matching Extendability of Harary Graphs

对Harary图的偶匹配可扩性进行了研究,得到结论:对于任意的n>1,仅当n=2,3时H3,2n是BM可扩图;对于任意的n(n≥3),H4,2n均不是BM可扩图;对于任意的n(n≥3),当n=3,4时,H5,2n是BM-可扩图;当n≥5时H5,2n不是BM可扩图;对于任意的n(n>3),r≥6时,Hr,2n是BM-可扩图等等.

In this paper, bipartite matching extendability of Harary graphs are studied. We have found that： For all integers n with n 〉1, H3.2n is bipartite matching extendable if and only if n ：2,3 ; For all integers n with n ≥3, H4.2n is not bipartite matching extendable; For all integers n with n ~3, Hs.2n is bipartite matching extendable if and only if n ： 3,4 ; For all integers zl with n ≥3, Hr.2n is bipartite matching extendable for all positive integers r （ 6 ≤ r ≤2n ）.