完全偶图的P_(2p)──分解

P_(2p)──Factorization of a Complete Bipartite Graph

利用图论中关于偶图的一个结论“Ks,s是 1 -可因子分解的”构造出当Km ,m有一个P2p 分解时 ,Kms,ms也有一个P2p分解 (当s是正整数 )。进一步我们还证明了Km ,n有一个P2 p 分解 ,当且仅当ⅰ >m =n ,ⅱ >m≡ 0 (modp ( 2 p -1 ) )。

By use of a result of bipartite graphs in the graph theory “ K s,s is 1-factorizable”,we concluded that if K m,m has a P 2p -factorization, then K ms,ms has a P 2p -factorization (for any positive integers).We also proved K m,n has a P 2p -factorization if and only if ⅰ> m=n,, ⅱ >m≡0( mod p(2p-1)) .