具有(k,r)-正交的(g,f)-因子分解的子图

(k,r)-Orthogonal (g,f)-Factorizations of Subgraph

研究了图的正交因子分解,通过构造函数p(x)和q(x),证明了(mg+k,mf-k)-图具有子图,该图有(g,f)-因子分解与kr-星(k,r)-正交,从而推广了原晋江教授的关于(mg+m-1,mf-m+1)-图,存在(g,f)-因子分解与星(m,r)-正交的结论.

The orthogonal factorizations of graphs were studied. By constructing functions p(x) and q(x), it was proven that there exists a subgraph of (mg+k,mf-k)-graph, and this subgraph has (g,f)-factorizations (k,r) orthogonal to a star with kr edges, which generalizes the result given by Professor Jing-jiang Yuan, i. e. , there exist (g,f)-factorizations (m,r)-orthogonal to star in a (mg+m-1 ,mf-m+1)-graph.