论文标题
覆盖部分度的两分图中指定的顶点的分离循环
Disjoint cycles covering specified vertices in bipartite graphs with partial degrees
论文作者
论文摘要
让$ k $成为一个积极的整数。让$ g $是订单$ 2N $的平衡的两部分图，带有两性$（x，y）$和$ x $的$ s $。假设每对非附属顶点$（x，y）$，$ x \ in s，y \ in y $ in y $ in y $ d（x）+d（y）\ geq n+1 $。我们表明，如果$ | s | \ geq 2k+2 $，则$ g $包含$ k $ discles Cycles覆盖$ s $的连接周期，以便每个$ k $ cycles中的每个循环都至少包含两个$ s $的顶点。在这里，最可能的是$ | s | $的学位状况和下限。而且我们还表明，如果$ | s | = 2k+1 $，则$ g $包含$ k $ discoint循环，使得$ k $循环中的每个循环中的每一个至少包含两个$ s $的顶点。
Let $k$ be a positive integer. Let $G$ be a balanced bipartite graph of order $2n$ with bipartition $(X, Y)$, and $S$ a subset of $X$. Suppose that every pair of nonadjacent vertices $(x,y)$ with $x\in S, y\in Y$ satisfies $d(x)+d(y)\geq n+1$. We show that if $|S|\geq 2k+2$, then $G$ contains $k$ disjoint cycles covering $S$ such that each of the $k$ cycles contains at least two vertices of $S$. Here, both the degree condition and the lower bound of $|S|$ are best possible. And we also show that if $|S|=2k+1$, then $G$ contains $k$ disjoint cycles such that each of the $k$ cycles contains at least two vertices of $S$.
